10. Lin and Andre biked home from school at a steady pace. Lin biked 1.5 km and it took her 5 minutes. Andre biked 2 km and it took him 8 minutes. a) Draw a graph with two lines that represent the bike rides of Lin and Andre. b) For each line, highlight the point with coordinates (1, k) and find k. c) Who was biking faster?

Applying the central angle theorem, we have:

a. angle BAC.

b. arc BEC

c. arc BC

d. Measure of arc BEC = 260°

e. Measure of arc BC = 100°

According to the central angle theorem, the central angle that is suspended at the center of a circle by two line segments (usually radii) have a measure that is equal to the measure of the intercepted arc. That is:

Measure of central angle = measure of intercepted arc.

A major arc have a measure that is greater than 180 degrees or half a circle, while minor arcs have a measure that is less than 180 degrees or half a circle.

a. A central angle in the image given is: angle BAC.

b. One major arc in the given circle is arc BEC (greater than half a half a circle/180 degrees).

c. One minor arc in the given circle is arc BC (less than half a half a circle/180 degrees).

d. m∠BEC = 360 - 100

m∠BEC = 260°

m∠BEC = measure of arc BEC [central angle theorem].

Measure of arc BEC = 260°

e. Measure of arc BC = m∠BAC [central angle theorem].

Measure of arc BC = 100°

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When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. Thus the required answer to the question is 990.

When a set of given numbers or items is to be arranged in a definite way or pattern, permutation can be used to determine the number of ways in which this can be done. The applicable formula is:

[tex]_{n} P_{r}[/tex] = [tex]\frac{n!}{(n - r)!}[/tex]

where: n is the total number of items given, and r is the number of items selected.

Thus the given question can be solved as :

[tex]_{11} P_{3}[/tex] = [tex]\frac{11!}{(11-3)!}[/tex]

       = [tex]\frac{11!}{8!}[/tex]

       = [tex]\frac{11 * 10 * 9 * 8!}{8!}[/tex]

       = 11 x 10 x 9

       = 990

[tex]_{11} P_{3}[/tex] = 990

Therefore, the required answer is 990.

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Answer:

6 * (5 + n)

Explanation:

Sum = addition

Difference = subtraction

Product = multiplication

Quotient = division

The initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

From the information given, we have the function to be;

a(t)=2400(1/2)^t/14

Where

To determine the initial amount, we have that t = 0

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{0}{14}[/tex]

[tex]A (t) = 2400[/tex]  × [tex]\frac{1}{2} ^0[/tex]

[tex]A (t) = 2400[/tex]

The initial amount is 2400 grams

For the amount remaining after 40 years, t = 40 years

A(t)=2400(1/2)^t/14

Substitute into the function, we have

[tex]A(t) = 2400[/tex] × [tex]\frac{1}{2} ^\frac{40}{14}[/tex]

[tex]A(t) = 2400[/tex] × [tex](0. 5) ^2^.^8^5^7[/tex]

[tex]A(t) = 2400[/tex] × [tex]0. 1380[/tex]

A(t) = 331. 26

A(t) = 331 grams in the nearest gram

Thus, the initial amount in the sample and the amount remaining after 40 hours are 2400 grams and 331 grams respectively.

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The number of kilometres travelled by the satellite in discuss in which case, the satellite makes 8 revolutions around the earth is; C = 177,271.8 km.

Given from the task content, the earth's diameter is; 6371 km and since, the height at which the satellite orbits the earth is; 343km, it follows that the diameter of orbit if the satellite in discuss is;

D = 6371 + (343)×2

Hence, we have; diameter, D = 7057 km.

Hence, the distance travelled after 8 revolutions is;

C = 8 × πd

C = 8 × 3.14 × 7057

C = 177,271.8 km.

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Answer:

16

Step-by-step explanation:

By the trapezoid midsegment theorem,

[tex]\frac{ST+6}{2}=11 \\ \\ ST+6=22 \\ \\ ST=16[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

We can use Trapezoid midsegment property:

[tex] \qquad❖ \: \sf \: \dfrac{ST + QR}{2} = LM[/tex]

[tex] \qquad❖ \: \sf \: \dfrac{ST + 6}{2} = 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =2 \times 11[/tex]

[tex] \qquad❖ \: \sf \: {ST + 6} =22[/tex]

[tex] \qquad❖ \: \sf \: {ST } =22 - 6[/tex]

[tex] \qquad❖ \: \sf \: {ST } =16[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

80 cups

Step-by-step explanation:

Answer:

9 Sahil has a fish tank in the shape of a cuboid, as shown in the diagram-- Diagram is NOT accurately drawn The tank is

55 cm long

28cm wide

cm 33 high The surface of the water in the tank is 3 cm below the top of the tank. Sahil is going to put some neon tetra fish in his tank. He must allow 4 litres of water for each of the neon tetra fish he puts in the tank. What is the greatest number of neon tetra fish Sahil can put in his tank?

Step-by-step explanation:

Answer:

To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.

The odds against selecting a red marble is =2/11

The number of marbles which were red = 9

The number of marbles which were blue = 2

The total amount of marbles in the Box = 11

When one marble is picked at random from the box, the odds against selecting a red marble can be gotten through the blue marble.

That is, the number of blue marble/ total marble

= 2/11

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The attached figure represents the array for 237 x 43

The array is given as:

237 x 43

An array is represented as:

Row x Column

This means that:

Row = 237

Column = 43

i.e. the array has 237 rows and 43 columns

The numbers are large, so the cells would be small when the arrays are drawn

See attachment for the array

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Using the z-distribution, it is found that a sample size of n = 18,805 is required.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]z = 2.81, \sigma = 24.4, M = 0.5[/tex].

Hence we solve for n to find the needed sample size.

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.5 = 2.81\frac{24.4}{\sqrt{n}}[/tex]

[tex]0.5\sqrt{n} = 24.4 \times 2.81[/tex]

[tex]\sqrt{n} = 48.8 \times 2.81[/tex]

[tex](\sqrt{n})^2 = (48.8 \times 2.81)^2[/tex]

n = 18,805.

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Answer:

Step-by-step explanation:

What if the estimate is within 1 of the population mean?

Answer:

[tex]y=\dfrac{8}{7}x - \dfrac{23}{7}[/tex]

Step-by-step explanation:

Rearranging the terms, we get [tex]7y=8x-23[/tex]. Dividing both sides by 7, we get [tex]\dfrac{7y}{7} = \dfrac{8x-23}{7}[/tex], so [tex]\boxed{y=\dfrac{8}{7}x - \dfrac{23}{7}}[/tex]

Answer:

y = [tex]\frac{8}{7}[/tex]x -[tex]\frac{23}{7}[/tex]

Step-by-step explanation:

You are changing this to the slope-intercept form of a line.

y = mx + b

8x -7y = 23  Subtract 8x from both sides of the equation

-7y = -8x + 23  Divide both sides of the equation by -7

y = [tex]\frac{-8}{-7}[/tex]  - [tex]\frac{23}{7}[/tex]  

[tex]\frac{-8}{-7}[/tex] is the same as [tex]\frac{8}{7}[/tex]

y = [tex]\frac{8}{7}[/tex]x - [tex]\frac{23}{7}[/tex]

13) 120 + 1.5 + 0.25 = 121.75 pounds

14) 4 - 1.5 = 2.5 pints

15) (2.25)(32)= $72

As per the unitary method, Mrs. Smith's current weight is 121 pounds and 3 ounces.

To find Mrs. Smith's current weight, we need to add the weight she gained over the last two months to her initial weight. First, we will convert the mixed fractions to improper fractions for easier calculations.

1½ pounds can be written as (2 * 1) + 1/2 = 3/2 pounds.

1/4 pound remains as it is.

Now, let's add the weight gained in the last two months:

3/2 pounds + 1/4 pound = (3/2) + (1/4) = (6/4) + (1/4) = 7/4 pounds.

Next, we add the total weight gained to Mrs. Smith's initial weight:

120 pounds + 7/4 pounds = (120 * 4/4) + (7/4) = (480/4) + (7/4) = 487/4 pounds.

To express the answer in pounds, we convert the improper fraction back to a mixed fraction:

487/4 pounds can be written as (4 * 121) + 3 pounds.

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Answer:

0.7

Step-by-step explanation:

Each increment is 0.1, so count the approximate number of increments needed to get from the orange circle on the left and the one on the right and multiply by 0.1 to get the difference.

Answer:

13

Step-by-step explanation:

The range of the data set can be defined as: max-min, and in a sorted data  set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.

With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.

This means the range is defined as: 30 - 17 = 13

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]

[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]

[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]

[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\text{24, 30, 17, 22, 22}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{30}[/tex]

[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]

[tex]\text{17}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\rm{30 - 17}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Using the arrangements formula, it is found that 1680 arrangements can be made with these numbers.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repeated elements, repeating [tex]n_1, n_2, \cdots, n_n[/tex] times, the number of arrangements is given by:

[tex]A_n^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

For the number 28535852, we have that:

Hence the number of arrangements is:

[tex]A_8^{3,2,2} = \frac{8!}{3!2!2!} = 1680[/tex]

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Answer:

  170

Step-by-step explanation:

The given relations can be used to write and solve an equation for the number of stickers Peter has.

Let p represent the number of stickers Peter has. That is twice as many as Joe, so Joe has (p/2) stickers. Joe has 40 more stickers than Emily, so the number of stickers Emily has is (p/2 -40).

The total number of stickers is 300:

  p +p/2 +(p/2 -40) = 300

  2p = 340 . . . . . . . . . . . . . . add 40, collect terms

  p = 170 . . . . . . . . . . . divide by 2

Peter has 170 stickers.

__

Additional comment

Joe has 170/2 = 85 stickers. Emily has 85-40 = 45 stickers.

We could write three equations in three unknowns. Solving those using substitution would result in substantially the same equation that we have above. Or, such a system of equations could be solved using a calculator's matrix functions, as in the attachment.

  p +j +e = 300

  p -2j +0e = 0

  0p +j -e = 40

Answer:

-5^x + 3x - 2.

Step-by-step explanation:

(f - g) (x) = f(x) - g(x)

=  -5^x - 4 - (-3x - 2)

= -5^x - 4 + 3x + 2

= -5^x + 3x - 2.

Answer: 1308m

Step-by-step explanation:

Top and Bottom: 19 x 16 x 2 = 608

Sides: 16 x 10 x 2 = 320

Front and Back: 19 x 10 x 2 = 380

608 + 320 + 380 = 1308

The inference is that the sum of the PPV and the false discovery rate for any test is always 100% because they complement each other.

When we add together the PPV and the false discovery rate for any test, the sum is always 100%.

It should be noted that the false discovery rate is the complement of the positive predicate value. The addition of their probability gives 100%.

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The expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of the exponent can be written as - (1/27).

Exponents are of the form aˣ, read as " a to the power x", function as a multiplied by itself x number of times, and are used in a numerical and algebraic expression.

To simplify these expressions, we use the following laws of the exponents:

[tex]1. a^m.a^n = a^{m + n}\\2.\frac{a^m}{a^n} = a^{m-n}\\ 3. (a^m)^n = a^{mn}\\4. a^{-m} = \frac{1}{a^m}\\5. a^0 = 1[/tex]

In the question, we are asked to simplify the expression, [tex](-243)^{-3/5}[/tex].

The expression can be solved using the laws of exponent as follows:

[tex](-243)^{-3/5}\\[/tex]

= [tex]((-3)^5)^{-3/5}[/tex]

= [tex](-3)^{-3}[/tex] {Using the law of exponent: [tex](a^m)^n = a^{mn}[/tex]}

= [tex]\frac{1}{-3^3}[/tex] {Using the law of exponent: [tex]a^{-m} = \frac{1}{a^m}[/tex]}

= 1/(-27)

= - (1/27).

Thus, the expression, [tex](-243)^{-3/5}[/tex] on simplification using the laws of exponent can be written as - (1/27).

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Answer:

[tex]3x^2[/tex]

Step-by-step explanation:

First main thing to know is the product and quotient rule of exponents.

Product Rule:

  [tex]x^a*x^b = x^{a+b}[/tex]

  And if this doesn't make sense, you can think of the exponent like this:

  [tex]x^a*x^b = (x*x*x*x...\text{ a amount of times}) * (x * x * x \text{ b amount of times})[/tex]

  and since multiplication is commutative, we can just combine all these x's, and since the total amount on the left is "a", and the right is "b", the total combined x's should be a+b, which can be expressed as:
   [tex]x*x*x... \text{ a+b amount of times}[/tex]

   which can be expressed as an exponent (x^(a+b))

Quotient Rule:

   [tex]\frac{x^a}{x^b} = x^{a-b}[/tex]

  You can use similar reasoning for this, since if you write it out you get

   [tex]\frac{x*x*x...\text{ a amount of times}}{x*x*x\text{ b amount of times}}[/tex]

  and since you have an x in the numerator and the denominator, you can simply cancel the x's out. In doing this you want to remove the denominator, so you cancel out "b" x's. So there will be (a-b) x's left in the numerator, and a 1 in the denominator, so it's just x^(a-b)

Ok so now let's apply these to solve your question

[tex]\frac{(15x^{-4})*x^{15}}{(5x^4)*x^5}\\[/tex]

So let's combine the exponents in the numerator and denominator using the product rule

[tex]\frac{15x^{11}}{5x^9}\\[/tex]

Now we can divide the 15 by 5, and divide the x^11 by the x^9 using the quotient rule

[tex]3x^2[/tex]

The histogram that correctly shows the data in the table is the histogram number four.

This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.

This data can be represented using ranges of temperature and the number o elements or substances in these ranges.

This data matches the fourth graph

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Answer: 1:52 PM

Step-by-step explanation:

PAULA: 2:14PM FINISHED THE RACE

BEATRICE: FINISHED 22 MINUTES EARLIER THEN PAULA

YOU TAKE 2:14PM AND SUBTRACT THE 22 MINS BEATRICE RAN TO GET YOU ANSWER.

SO 2:14 -14 MINS=2:00PM 14+8=22 (THE MINS BETRICE FINISHED)

2:00-8 MINS ( REMAINING FROM THE 22 ) THEN 2:00-8 MINS =1:52

ANSWER:1:52PM

Answer:

-13

Step-by-step explanation:

-2x6 = -12

-9+8= -1

-1+-12=-13

Hope this helps

The value of surface integral using the Divergence Theorem is [tex]729\pi[/tex] .

Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:[tex]\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS[/tex]

The divergence of F is

[tex]div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z[/tex]

[tex]div F=6x^{2}+3y^{2}+3y^{2}[/tex]

Let E be the region [tex]{(x,y,z):0\leq z\leq 9-x^{2} -y^{2}[/tex] then by divergence theorem we have [tex]\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV[/tex]

Now we find the value of the integral:

[tex]=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\[/tex]

[tex]=2\pi\times \frac{729}{2}\\=729\pi[/tex]

Thus we can say that the value of the integral for the surface around the paraboloid is given by [tex]729\pi[/tex].

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Answer:

[tex]x=2^{\frac{2}{3}}[/tex]

Step-by-step explanation:

1) Add 8 to both sides.

[tex]2x^3=8[/tex]

2) Divide both sides by 2.

[tex]x^3=\frac{8}{2}[/tex]

3) Simplify [tex]\frac{8}{2}[/tex] to 4.

[tex]x^3=4[/tex]

4) Take the cube root of both sides.

[tex]x=\sqrt[3]{4}[/tex]

5) Rewrite 4 as 2².

[tex]x=\sqrt[3]{2^2}[/tex]

6) Use this rule: [tex]{({x}^{a})}^{b}={x}^{ab}[/tex].

[tex]x=2^{\frac{2}{3}}[/tex]

Decimal Form: 1.587401

__________________________________________

Check the answer:

[tex]2x^3-8=0[/tex]

1) Let [tex]x=2^\frac{2}{3}[/tex].

[tex]2(2^{\frac{2}{3} })-8=0[/tex]

2) Use this rule: [tex](x^a)^b=x^{ab}[/tex].

[tex]2\times2^{\frac{2\times3}{3} } -8=0[/tex]

3) Simplify 2 * 3 to 6.

[tex]2\times2^{\frac{6}{3} } - 8 =0[/tex]

4) Simplify 6/3 to 2.

[tex]2\times2^2-8=0[/tex]

5) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].

[tex]2^3-8=0[/tex]

6) Simplify 2^3 to 8.

8 - 8 = 0

7) Simplify 8 - 8 to 0.

0 = 0

Thank you,

Eddie