Mathematics College
Answers
Answer 1
We have a circle, where a fraction is shaded.
The not-shaded fraction is the sum of 4/9 and 1/2. These fraction represent the fraction of the circle area (you can see it clearly with "one half" fraction).
Then, if we substract from 1, the complete circle, the not shaded parts (4/9+1/2), we should get the shaded fraction:
[tex]1-(\frac{4}{9}+\frac{1}{2})=1-\frac{4\cdot2+1\cdot9}{18}=1-\frac{8+9}{18}=1-\frac{17}{18}=\frac{18-17}{18}=\frac{1}{18}[/tex]
The shaded part represents 1/18 of the circle.
Related Questions
5 children want to share 20 apples equally. how many apples will each child get?
Answers
[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]
A helicopter rose vertically 10 miles and then flew west 13 miles. About how far was the helicopter from the starting point?
Answers
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
Complete thissequence.-30, -22,-14, -6,2 , [?]Enter the number that goes in the green box.
Answers
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
find the acute angle lies between the vectors a=3i+4j and b=7i+j
Answers
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°
Find the area of the shaded sector of the circle show all of your work write your answer in terms of pi
Answers
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]
A gardener has 13 identical looking tulip bulbs, of which 6 will produce yellow tulips and 7 will become pink. she randomly selects and plants 6 and gives the rest away. When the tulips start to bloom, what is the probability that all are yellow?
Answers
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.
* 1 point Important: Look at Example #5 for worked out example and Task Criteria Which graph represents the solution of -9x + 4y s8 ? 1) 8 2 4 6 8 y 2) 2 24 3) 2 4 6 8 4)
Answers
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
Please help, due in 10 mins I'm just making sure my answer is correct, if it's not can you correct me?
Answers
The amount spent is 96.
Cost of each tan is 24
Number can be calculated as,
[tex]24x=96[/tex]
first option is correct
Al saves pennies. He agreed to give 1/2 of his pennies to Bev is she would give 1/2 of what she got from Al to Carl and if Carl in turn would give 1/2 of what he got from Bev to Dani. Bev, Carl, and Dani agreed and Dani received 6 pennies. How many pennies did Al have initially?
Answers
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:
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Find the value of cos210°
Answers
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
Answers
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
What is the volume of this rectangular prism? 5/4 cm 5/3 cm 5/2 cm
Answers
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.
The pair of figures to the right are similar. What is the ratio of the perimeters and the ratio of the areas?The ratio of the perimeters is (Simplify your answer.)The ratio of the areas is 1. (Simplify your answer.)
Answers
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.
Select the correct answer.
If f(x) = |x|, which equation describes the graphed function?
Answers
Answer:
D is correct.
Step-by-step explanation:
[tex]f(x) = |x| [/tex]
[tex]3 - f(x) = 3 - |x| [/tex]
So D is correct.
2 ft 9 in / 4 ft 7 in = 2.4 cm / x
Answers
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
In a right triangle,the altitude q from the right angle to the hipotenuse divides..........
Answers
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]
Question 6 (1 point(-1,1)(1, -1)Mach MLXBlank 1
Answers
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
Mal is going for a walk. She walks at a constant speed for 20mins. She takes a break for 5 mins before turning around and walking back home she walks faster than she did before
Answers
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]
Find the area of the figure below. below. 24 yd 24 yd I 24 yd 40 yd 576
Answers
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
Function 1Function 2f(x)=3x? - 12x+13(-2,5)(a) What is the vertex of Function 1?osX 미미?(b) What is the vertex of Function 2?OD(c) Which function has the smaller minimum value?Function 1Function 2What is the smaller minimum value?CheckSave
Answers
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
A single die is rolled three times. What is the probability that a 5 will show on the upward face at least once?
Answers
Answer:
32.3%.
Step-by-step explanation:
on a survey 7 students reported how many minutes it takes them to travel to school. 6,5,16,3,12,15,8find the Mean travel time of the students round to the nearest 10th if necessary
Answers
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
PART BA student is in the process of solving an equation. The original equations and the first step are shown below.Original : 4(a - 1) +3 = 18Step one: 4(a - 1) = 15Which property did the student use for the first step? Explain why this property is correct.f+BI U S XX,Font FamilyFont SizesАА
Answers
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.
1) A hairdresser uses 800ml of shampoo and 320 ml of conditioner on a daily basis. Write in its simplest form the ratio of shampoo to conditioner 2) sugar and flour are mixed in the ratio 2:3 how much sugar is used with 600g of flour?
Answers
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.
Julio has $40.00 to rent bikes for himself and a friend for 5nhours. Each bike rental cost s $3.25 per hour.the 2 friends need a total of 32.50 to rent bikes for 5 hours.therefore blank1.251.752.003.257.508.2536.75whats the answer
Answers
Student not ready. The question is missing!
Practice writing and evaluating powers.AssignmentUse the expression to complete the statements.(0.5)10(0.5)10 is the(0.5) is theof (0.5)1010 is the✔ of (0.5) 10A power is another way to writeThe choices for 1,2 and 3 are:BaseExponent PowerThe choices for the last one are: Repeated addition,repeated division,repeated multiplication,repeated subtraction
Answers
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.
A company has 9 male and seven female employees and needs to nominate two men and two women for the company bowling team how many different teams can be formed?
Answers
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.
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y < 1/3x - 2y ≤ -1/6x - 5
Answers
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 interior lines are they congruent or supplementary
Answers
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
From the 6 male and 11 female salesrepresentatives for an insurancecompany, a team of 4 men and 2women will be selected to attend anational conference on insurancefraud.
Answers
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]