How Much Of The Circle Is Shaded? Write Your Answer As A Fraction In Simplest Form.4/9 1/2 (2024)

[tex]\begin{gathered} \text{We have to divide 20 into 5, that is} \\ \frac{20}{5}=4 \\ \\ \text{ Each child will get 4 apples} \end{gathered}[/tex]

the situation forms a right triangle.

We have to find x

Apply the Pythagorean theorem:

c^2 = a^+b^2

Where:

c= hypotenuse (x) , the longest side

a & b = the other 2 legs of the triangle

Replacing:

x^2 = 13^2 + 10^2

Solve for x

x^2 = 169 + 100

x^2 = 269

x = √269

x= 16.4 miles

SOLUTION

We want to complete the sequence below.

-30, -22, -14, -6, 2

From the sequence above, we can see that

[tex]\begin{gathered} -30+8=-22 \\ -22+8=-14 \\ -14+8=-6 \\ -6+8=2\text{ and finally } \\ 2+8=10\text{ } \end{gathered}[/tex]

So the common difference is 8.

Hence the answer is 10

Answer:

The acute angle lies between the vectors a=3i+4j and b=7i+j is 45°

Explanation:

The given vectors are:

a = 3i + 4j

b = 7i + j

The acute angle between vectors a and and b is given by the formula:

[tex]\theta=\cos ^{-1}\frac{a.b}{|a\mleft\Vert b\mright|}[/tex]

The scalar product of vectors a and b is:

a.b = (3i + 4j).(7i + j)

a.b = (3x7) + (4x1)

a.b = 21 + 4

a.b = 25

The magnitude of a is:

[tex]\begin{gathered} |a|=\sqrt[]{3^2+4^2} \\ |a|=\sqrt[]{9+16} \\ |a|=\sqrt[]{25} \\ |a|=5 \end{gathered}[/tex]

The magnitude of b is:

[tex]\begin{gathered} |b|=\sqrt[]{7^2+1^2} \\ |b|=\sqrt[]{49+1} \\ |b|=\sqrt[]{50} \\ |b|=5\sqrt[]{2} \end{gathered}[/tex]

Substituting the values of a.b, |a|, and |b| into the formula for the acute angle.

[tex]\begin{gathered} \theta=\cos ^{-1}\frac{a.b}{|a\Vert b|} \\ \theta=\cos ^{-1}\frac{25}{5\times5\sqrt[]{2}} \\ \theta=\cos ^{-1}\frac{25}{25\sqrt[]{2}} \\ \theta=\cos ^{-1}\frac{1}{\sqrt[]{2}} \\ \theta=45^0 \end{gathered}[/tex]

Therefore, the acute angle lies between the vectors a=3i+4j and b=7i+j is 45°

explanation

We are to find the area of the shaded sector

To do s,w e will have to use the formula:

[tex]\frac{\theta}{360}\times\pi r^2[/tex]

in our case, the central angle is a major angle

[tex]\begin{gathered} \theta=360-90=270 \\ r=18ft \end{gathered}[/tex]

Thus, we will have

[tex]\frac{270}{360}\times\pi\times18^2=243\times\pi=243\pi[/tex]

Thus, the answer is

[tex]243\pi[/tex]

Given data:

The total numbbers of bulbs are n=13.

The expression for the probability that gardener plants 6 yellow bulbs is,

[tex]\begin{gathered} P=\frac{6}{13}\times\frac{5}{12}\times\frac{4}{11}\times\frac{3}{10}\times\frac{2}{9}\times\frac{1}{8} \\ =\frac{1}{13\times11\times3\times4} \\ =\frac{1}{1716} \end{gathered}[/tex]

Thus, the probability that gardener plants 6 yellow bulbs is 1/1716.

Answer

Option 2

Explanation:

Given the following inequality

[tex]-9x\text{ + 4y }\leq\text{ 8}[/tex]

Step 1: Turn the inequality to an equation

The inequality becomes

-9x + 4y = 8

Step 2: find the x and y - intercepts

To find the y - interecpts, make x = 0

-9x + 4y = 8

make x = 0

-9(0) + 4y = 8

0 + 4y = 8

4y = 8

Divide both sides by 4

4y/4 = 8/4

y = 2

When x = 0 y= 2 ------------------- (0, 2)

Find x - intercept

Make y = 0

-9x + 4y = 8

-9x + 4(0) = 8

-9x + 0 = 8

-9x = 8

Divide both sides by -9

-9x / -9 = 8/-9

x = -8/9

x = - 0.888

Therefore, x = -0.888 or -8/9 when y = 0

(-8/9, 0)

Step 3: Graph the points

Therefore, the answer is option 2

The straight line is thick because the inequality sign is is less than or equal to

Also, the inner part of the graph was shaded because the function is less than or equal to the point

The amount spent is 96.

Cost of each tan is 24

Number can be calculated as,

[tex]24x=96[/tex]

first option is correct

ANSWER

[tex]48\text{ pennies}[/tex]

EXPLANATION

Let the number of pennies Al has be x.

Bev gave 1/2 of what she got from Al to Carl, which means that Bev gave:

[tex]\begin{gathered} \frac{1}{2}\cdot\frac{1}{2}\cdot x \\ \Rightarrow\frac{1}{4}x \end{gathered}[/tex]

Carl gave 1/2 of what he got from Bev to Dani, which means that Carl gave:

[tex]\begin{gathered} \frac{1}{2}\cdot(\frac{1}{4}x) \\ \Rightarrow\frac{1}{8}x \end{gathered}[/tex]

That is the number that Dani received.

We have that Dani received 6 pennies which means:

[tex]\frac{1}{8}x=6[/tex]

Solve for x by multiplying both sides by 8:

[tex]undefined[/tex]

ANSWER

[tex]\begin{equation*} -\frac{\sqrt{3}}{2} \end{equation*}[/tex]

EXPLANATION

We want to find the value of:

[tex]\cos210[/tex]

We can rewrite it as:

[tex]\cos(180+30)[/tex]

Because 210 degrees is in the third quadrant, the value of its cosine is negative and it is the same magnitude as the cosine of 30 degrees.

In other words, the value of cos210 is:

[tex]\cos(210)=-\cos(30)=-\frac{\sqrt{3}}{2}[/tex]

That is the answer.

6-k divided by 5/7 k=1/6 is 49/6=7 7/6

Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

What is Division?

In this example, the number being divided (15) is known as the dividend, and the number being divided by (3 in this instance) is known as the divisor.

6 -k /5/7\s6-1/6 /5/7\s36-1/6 /5/7\s35/6 *7/5\s49/6=7 7/6.

Chunking Technique. The repeated subtraction method is another name for the chunking approach.

Method of Short Division (Bus Stop Method)Method of long division.A good chunking example.Short division method illustration.long division illustrations

Dividend, quotient, and divisor are the three main components of division. Additionally, we obtain a non-zero remainder as the fourth component of the division when the divisor is not a dividend factor.

To learn more about Division refer to:

https://brainly.in/question/11095543

#SPJ1

Given data:

The given dimension of the rectangular prism is 5/4 cm x 5/3 cm x 5/2 cm.

The expression for the volume is,

[tex]\begin{gathered} V=(\frac{5}{4}\text{ cm)(}\frac{5}{3}\text{ cm)(}\frac{5}{2}\text{ cm)} \\ =\frac{125}{24}cm^3 \end{gathered}[/tex]

Thus, the volume of the rectangular prism is 125/24 cubic-cm.

As per given by the question,

There are given that two similar figure.

Now,

From the the figure,

First find the perimeters of the both figure.

So,

From the formula of perimeters of the square,

[tex]P=\text{Sum of all sides}[/tex]

Then,

The ratiio of the perieters of the both figure is,

[tex]\begin{gathered} P=\frac{\text{Sum of all side in figure 1}}{Sum\text{ of all side in figure 2}} \\ =\frac{9+9+9+9}{15+15+15+15} \end{gathered}[/tex]

Then,

[tex]\begin{gathered} P=\frac{9+9+9+9}{15+15+15+15} \\ =\frac{36}{60} \\ =\frac{3}{5} \end{gathered}[/tex]

Now,

From the formula of the area of the given figure.

[tex]A=(side)^2[/tex]

Then,

The ratiao of the area of the given figure is,

[tex]\begin{gathered} A=\frac{(sideoffigure1)^2}{(sideoffigure2)^2} \\ A=\frac{(9)^2}{(15)^2} \end{gathered}[/tex]

Then,

[tex]\begin{gathered} A=\frac{(9)^2}{(15)^2} \\ =\frac{81}{225} \\ =\frac{9}{25} \end{gathered}[/tex]

Hence, the ratio of the perimeters of the given figure is 3/5, and the ratio of the area of the of given figure is 9/25.

Answer:

D is correct.

Step-by-step explanation:

[tex]f(x) = |x| [/tex]

[tex]3 - f(x) = 3 - |x| [/tex]

So D is correct.

Solution:

Given:

[tex]\frac{2ft\text{ }9in}{4ft\text{ }7in}=\frac{2.4cm}{x}[/tex]

To solve for x, we take the units to the same quantity.

Converting all units to centimeters,

[tex]\begin{gathered} 1ft=30.48cm \\ 1in=2.54cm \\ \\ Hence, \\ 2ft\text{ }9in=2(30.48)+9(2.54)=60.96+22.86 \\ 2ft\text{ }9in=83.82cm \\ \\ \\ Also, \\ 4ft\text{ }7in=4(30.48)+7(2.54)=121.92+17.78 \\ 4ft\text{ }7in=139.7cm \end{gathered}[/tex]

Hence:

[tex]\begin{gathered} \frac{2ft\text{ }9in}{4ft\text{ }7in}=\frac{2.4cm}{x} \\ \frac{83.82cm}{139.7cm}=\frac{2.4cm}{x} \\ \\ Cross\text{ multiplying the equation:} \\ 83.82\times x=139.7\times2.4 \\ x=\frac{139.7\times2.4}{83.82} \\ x=\frac{335.28}{83.82} \\ x=4cm \end{gathered}[/tex]

Therefore, x = 4cm

Then we have the next equivalence

[tex]\frac{4}{q}=\frac{q}{16}[/tex]

then we need to isolate the q

[tex]\begin{gathered} q^2=4\cdot16 \\ q^2=64 \\ q=\sqrt[]{64} \\ q=8 \end{gathered}[/tex]

We have to find the slope having points (-1,1) and (1,-1), We are going to use the formula for the slope of the line

[tex]m=\frac{y2-y1}{x2-x1}=\frac{-1-1}{1-(-1)}=\frac{-2}{2}=-1[/tex]

The answer is m= -1

Since the walks faster going back home , the slope will be steeper and is negative and it will take lesser time for her to get back that is, the time will be lesser than the initial 20 minutes she started with

Since she walked faster going back home, it will take her less than 20 minutes to go back home.

The total time for the journey should be

[tex]\begin{gathered} 20+5+15=40\text{ minutes} \\ so\text{ she should take }\approx\text{ 15 minutes to get back home if she will not rest on the road going back} \end{gathered}[/tex]

This figure is formed by a rectangle of 40 by 24 yd and a square of 24 by 24 yd

Rectangle area = 40 x 24 = 960

Square area = 24 x 24 = 576

Total area = 960 + 576 = 1536 square yards

Ans

a) (-2,

b) (2, 1)

Explanation:

a) Since you have gotten the vertex of function 1: (-2, 5)

b) To get the vertex of 2, we would plot the graph of the function: f(x)=3x^2 - 12x+13

The graph opens up: the vertex is at the lowest point on the graph

This is at (2, 1)

c) The function with the smaller minimum value is function 2

The y value of function 1 = 5

The y value of function 2 = 1

d) The minimum value = 1

Answer:

32.3%.

Step-by-step explanation:

As given by the question

There are given that the survey of 7 students:

[tex]6,\text{ 5, 16, 3, 12, 15, 8}[/tex]

Now,

From the formula to find the mean:

[tex]\operatorname{mean}=\frac{\text{Addition of the total given data}}{\text{Total number of data}}[/tex]

Then,

[tex]\operatorname{mean}=\frac{6+5+16+3+12+15+8}{7}[/tex]

Then,

[tex]\begin{gathered} \operatorname{mean}=\frac{6+5+16+3+12+15+8}{7} \\ \operatorname{mean}=\frac{65}{7} \\ \operatorname{mean}=9.3 \end{gathered}[/tex]

Hence, the mean travel time is 9.3 minutes

As per given by the question,

There are given that a original form is,

[tex]4(a-1)+3=15[/tex]

Now,

The first step of the given equation is,

[tex]\begin{gathered} 4(a-1)+3=15 \\ 4a-4+3=15 \end{gathered}[/tex]

Then,

The value of the given equation is,

[tex]\begin{gathered} 4a-1=15 \\ 4a=15+1 \\ 4a=16 \end{gathered}[/tex]

So, here distributive properties used by the student to solving the first step.

Hence, the first step is 4a-4+3=15.

Given:

1) A hairdresser uses 800ml of shampoo and 320 ml of conditioner on a daily basis.

The ratio from a to b is writtenn as,

[tex]a\colon b\text{ that is }\frac{a}{b}[/tex]

So, the ration of shampoo to the conditioner is,

[tex]\frac{800}{320}=\frac{5}{2}[/tex]

Answer: 5:2.

2) sugar and flour are mixed in the ratio 2:3

[tex]\text{sugar:flour}=2\colon3[/tex]

Let x be the amount of sugar is used with 600 g of flour.

[tex]\begin{gathered} \frac{2}{3}=\frac{x}{600} \\ 2\times600=3x \\ 1200=3x \\ x=\frac{1200}{3} \\ x=400\text{ g} \end{gathered}[/tex]

Answer: 400 g of suger is used.

By definition, a Power has the following form:

[tex]b^n^{}[/tex]

Where "b" is the base and "n" is the exponent.

Powers represent repeated multiplication. For example:

[tex]2^3=2\cdot2\cdot2=8[/tex]

In this case, you have the following Power:

[tex](0.5)^{(10)}[/tex]

Based on the explained above, you can identify that:

- The base of the Power is:

[tex]0.5[/tex]

- And the exponent is:

[tex]10[/tex]

Therefore, that means that to get the result, you must multiply 10 times the base 0.5

The answers are:

1. Power.

2. Base.

3. Exponent.

4. Repeated multiplication.

Explanation

The number of different teams that can be formed is given by the product of two numbers:

1. The number of different ways that 2 male employees can be selected.

2. The number of different ways that 2 female employees can be selected.

The first number is given by all the possible ways to select 2 males out of 9 without caring about the order. This last part basically means that even though there are two ways to select two particular males (let's name them A and B), which are AB and BA, they count as a single way. This implies that what we are looking for is the total number of combinations. In general, the total number of combinations when selecting k items from a total of n is given by:

[tex]_nC_k=\frac{n!}{(n-k)!k!}[/tex]

Then the number of different ways that 2 male employees can be selected is given by:

[tex]_9C_2=\frac{9!}{(9-2)!2!}=\frac{9!}{7!2!}=36[/tex]

For the number of different ways that 2 female employees can be selected we can do the same. The only difference is that here we have a total of 7 people to select from:

[tex]_7C_2=\frac{7!}{(7-2!)2!}=\frac{7!}{5!2!}=21[/tex]

Then the number of different teams that can be formed is given by the product of the two numbers that we found:

[tex]N=36\cdot21=756[/tex]Answer

Then the answer is 756.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

y < 1/3x - 2

y ≤ -1/6x - 5

Step 02:

system of inequalities:

ineq. 1:

y < 1/3x - 2

graph the line 1:

y = 1/3x - 2

if x = 0:

y = 1/3(0) - 2 = 0 - 2 = - 2

(0, -2)

if y = 0:

[tex]\begin{gathered} 0\text{ =}\frac{1}{3}x-2 \\ 2=\frac{1}{3}x \\ 2\cdot3=x \\ 6\text{ = x} \end{gathered}[/tex]

(6, 0)

ineq. 2:

y ≤ -1/6x - 5

graph the line 2:

y = -1/6x - 5

if x = 0:

y = -1/6(0) - 5 = 0 - 5 = - 5

(0 , -5)

if y = 0:

[tex]\begin{gathered} 0\text{ =- }\frac{1}{6}x-5 \\ 5=-\frac{1}{6}x \\ 5\cdot(-6)\text{ = x} \\ -30\text{ = x} \end{gathered}[/tex]

(-30 , 0)

graph solution:

The answer is:

The solution to the system: Unbounded

Alternate angles are angles that are in opposite positions relative to a transversal intersecting two lines. If the alternate angles are between the two lines intersected by the transversal, they are called alternate interior angles.

m<1 and m< 2 are equal

Alernate interior angles are congruent

Answer:

[tex]825\text{ ways}[/tex]

Explanation:

Here, we want to get the number of ways in which the team of 6 will be selected

From the question, out of 6 males, 4 will be selected, while out of 11 females, 2 will be selected

To select r from a total of n, we use the following formula:

[tex]^nC_r\text{ = }\frac{n!}{(n-r)!r!}[/tex]

Selecting 4 out of 6, we have:

[tex]^6C_4\text{ = }\frac{6!}{(6-4)!4!}\text{ = 15}[/tex]

For the second part, we are selecting 2 out of 11, we have that as:

[tex]^{11}C_2\text{ = }\frac{11!}{(11-2)!2!}\text{ = 55}[/tex]

The total number of ways will be the product of the two as follows:

[tex]55\times15\text{ = 825 ways}[/tex]