Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.
Answers
Answer:
To show: [tex]\sqrt{21}[/tex] is between 4 and 5
We know:
21 is lies between two consecutive integer i.e, 16 and 25
We can write this as:
[tex]16 < 21 < 25[/tex]
or
[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]
Simplify:
[tex]4 < \sqrt{21} < 5[/tex]
⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.
Therefore, [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.
Answer:
We know that
[tex]16<21<25[/tex]
Because, 16 is less than 21 and 25 is more than 21.
Now, if we apply a square root to each part, we would have
[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]
Then, we solve each square root, except the square root of 21, because it doesn't have an exact result
[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]
So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.
Related Questions
The area of a rectangle is 28 ft2 , and the length of the rectangle is 1 ft more than twice the width. find the dimensions of the rectangle.
Answers
L=2x+1
Area=(2x+1)x=28
2x²+x=28
2x²+x-28=0
(2x-7)(x+4)=0
x=3.5, -4. (3.5 makes more sense)
2x+1=8
area = 28 ft²
width = 3.5 feet | length = 8 feet.
The length is 8feet and the width of the rectangle is 3.5feet
Let the width of the rectangle be represented by w
Let the length of the rectangle be represented by = 2w + 1
Therefore, based on the information given, the equation to solve the question will be:
w(2w + 1) = 28
2w² + w = 28
2w² + w - 28 = 0
2w² + 8w - 7w - 28 = 0
2w(w + 4) - 7(w + 4) = 0
2w - 7 = 0
2w = 0 + 7
2w = 7
w = 7/2
w = 3.5
The width is 3.5 feet
The length will be:
= 2w + 1
= 2(3.5) + 1
= 7 + 1
= 8
The length is 8feet and the width is 3.5feet
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Chase answers 3/4 of his math questions correctly. There were 40 questions on the test.
a. How many did he get right?
b. How many did he miss?
Answers
multiply 40 by 3/4
40 x 3/4 = 40*3 = 120, 120/4 = 30
he answered 30 correctly
40-30 = 10, he missed 10
The temperature of a point $(x,y)$ in the plane is given by the expression $x^2 + y^2 - 4x + 2y$. what is the temperature of the coldest point in the plane?
Answers
can be written as follows:
[tex] x^{2} -4x+ y^{2}+2y[/tex]
[tex](x^{2} -4x+4)-4+ (y^{2}+2y+1)-1[/tex]
[tex] (x-2)^{2}+(y+1)^{2} -5[/tex]
since [tex](x-2)^{2}[/tex] and [tex](y+1)^{2}[/tex] are always positive, except for x=2 and y=-1, when they become 0,
the minimum value of this expression is when x=2, and y=-1, that is -5
Answer: -5
In triangle PQR, C is the centroid.
Answers
Question (a):
PC:CY = 2:1
If CY=10, then PC=20 and PY=20+10=30
Question (b):
QC:CZ= 2:1
If QC=10, then CZ=5 and ZQ=10+5=15
Question (c):
PX : XQ = 1 : 1
if PX = 20, then PQ = 40
two points are collinear
Answers
Answer:
1. B
2. C
3. B
4. C
5. A
6. A
7. C
8. A
9. D
10. C
11. B
12. B
Two minor league baseball players got a total of 292 292 hits. washington had 18 18 more hits than sanchez. find the number of hits for each player
Answers
Number of hits by Washington = 18 + x
Total number of hits = 292
x + 18 + x = 292
2x + 18 = 292
2x = 274
x = 137
Hence, Sanchez has 137 hits and Washington has 155 hits.
Jackie walks into a convenience store and recognizes the number of lottery tickets she can purchase varies inversely with the price of each ticket. If Jackie buys $5 tickets, she can purchase exactly 6 tickets. If she buys $3 tickets, what is the maximum number of tickets she can purchase?
Answers
When the y inversely proportioned to x, the equation is
y = k/x where k is a constant
We work out the value of k by using the information y = 6 and x = 5
6 = k/5
k = 30
Hence, the maximum number of tickets when the price is $3 is
y = 30/3
y = 10 tickets
Answer:
Step-by-step explanation:
10
The screen on Lawrence's new phone is 3.15 centimeters long.What mixed number represent the lenght of the phone screen?
Answers
One example of mixed number is [tex]3 \frac{1}{4} [/tex], read as 'three and one quarter'. As decimal fraction, [tex]3 \frac{1}{4} [/tex] equals to 3.25
We are given the value of 3.15 and to change this into a mixed number, first note the whole number, which is 3.
We then change the decimal value 0.15 into a fraction and it is [tex] \frac{15}{100}= \frac{3}{20} [/tex]
Hence, 3.15 = [tex]3 \frac{3}{20} [/tex]
if acircle is inscribed in a hexagon, which of the following must be true ? Check all that apply.
A. The hexagon is circumscribed about the circle.
B. Each vertex of the hexagon lies inside the circle.
C. The circle is congruent to the hexagon.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Answers
D. Each vertex of the hexagon lies outside the circle .
E. The circle is tangent to each side of the hexagon .
Answer: A. The hexagon is circumscribed about the circle.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.
Step-by-step explanation:
Given: A circle is inscribed in a hexagon.
Then the hexagon is circumscribed about the circle.
Each vertex of hexagon lies outside the circle.
As each side of hexagon is just attached to the circle not passing through the circle, thus the circle is tangent to each side of the hexagon.
Since circle is a closed curve and hexagon is regular polygon with 6 sides, they cannot be congruent because they have different shapes.
In a genetics experiment on? peas, one sample of offspring contained 402402 green peas and 3838 yellow peas. based on those? results, estimate the probability of getting an offspring pea that is green. is the result reasonably close to the value of 3 divided by 43/4 that was? expected?
Answers
The empirical probability of getting a green pea is approximately 91.37%, which is not reasonably close to the expected value of 75% based on Mendel's laws.
Explanation:In this observed pea experiment, there were 402 green peas and 38 yellow peas. To calculate the probability of getting a green pea, we divide the number of green peas by the total number of peas. Therefore, the probability is 402/(402+38) ≈ 0.9137 or 91.37%, which is the empirical probability of getting a green pea.
The expected ratio, which is based on Mendel's genetic laws, is 3/4 for the dominant trait (green peas in this case) but after doing the math, it represents 0.75 or 75%, which is lower than our empirical probability. Therefore, the result is not reasonably close to the value expected (3/4).
It's worth mentioning that this discrepancy can occur due to many reasons including statistical variation, "especially when sample size is not large enough".
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Write a function max that has two c string parameters and returns the larger of the two.
Answers
if (strcmp(number1, number2) > 0)
return number1;
else
return number2;
}
Final answer:
To determine the larger of two C strings, a function named max uses strcmp to compare them, returning the one considered greater in alphabetical order.
Explanation:
To write a function named max that returns the larger of two C strings, one must compare the two strings alphabetically. Here is an example implementation in C:
#include // Include the header file for string functions// Function declaration
const char* max(const char* str1, const char* str2) {
// Compare the two strings
int result = strcmp(str1, str2);
// If str1 is greater than or equal to str2
if(result >= 0)
return str1;
else
return str2;
}
The strcmp function from the string.h library is used to perform the comparison. If the first string (str1) is greater than or equal to the second string (str2), str1 is returned; otherwise, str2 is returned. Note that the comparison is based on the ASCII values of the characters, effectively ordering them alphabetically.
When a meteorologist says that there is a 30% chance of showers, what type of probability is the person using?
Answers
A basketball court is in the shape of a rectangle. It has a length of (x − 7) meters and a width of (x + 3) meters. The expression below represents the area of the court in square meters:
(x − 7)(x + 3)
Which of the following simplified expressions represents the area of the basketball court in square meters?
− 6x + 3
x2 − 21
x2 − 4x − 21
x2 − 7x + 3
Answers
The answer is x² - 4x - 21 or C
The area (A) of the rectangle is:
A = l * w (l - length, w - width)
We have:
l = x - 7
w = x + 3
Therefore:
A = (x - 7)(x + 3)
Now, multiply each factor with another:
A = (x - 7)(x + 3) = x * x + x * 3 - 7 * x - 7 * 3 = x² + 3x - 7x - 21 = x² - 4x - 21
15,000 loses value by 20% each year. What is the value after 3 years
Answers
Answer:
Step-by-step explanation: 7680
After losing 20% we have 80% remaining
∴ value after three years = 15,000 × [tex]\frac{80}{100}[/tex] × [tex]\frac{80}{100}[/tex] ×[tex]\frac{80}{100}[/tex]
= 15,000 × [tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex] ×[tex]\frac{4}{5}[/tex]
= 7680
I'm in desperate need of help please !!
Answers
[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\qquad \begin{cases} year\ 0\\ -----\\ t=0\\ A=42679 \end{cases} \\\\\\ 42679=Ie^{k0}\implies 42679=I\cdot 1\implies 42679=I\qquad thus \\\\\\ \boxed{A=42679e^{rt}}[/tex]
now, let's fast-forward 8 years later, t = 8, the population has dropped to 33247, so A = 33247, what's "r", or in your paper, it uses "k", anyhow, is just the rate.
[tex]\bf A=42679e^{rt}\qquad \begin{cases} t=8\\ A=33247 \end{cases}\implies 33247=42679e^{r8} \\\\\\ \cfrac{33247}{42679}=e^{8r}\impliedby \textit{let's now take \underline{ln} to both sides} \\\\\\ ln\left( \frac{33247}{42679} \right)=ln(e^{8r})\implies ln\left( \frac{33247}{42679} \right)=8r\implies \cfrac{ln\left( \frac{33247}{42679} \right)}{8}=r \\\\\\ -0.0312178\approx r\qquad now\ 100\cdot r\approx -3.1\%[/tex]
is a negative rate, because, the population is decreasing.
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8)
how many days does it take for 60% of the population to know about the crime? well, what's 60% of 1,150,000? well (60/100) * 1,150,000, or 69000.
[tex]\bf P(t)=1150000e^{-0.03t}\implies 690000=1150000e^{-0.03t} \\\\\\ \cfrac{690000}{1150000}=e^{-0.03t}\implies \cfrac{3}{5}=e^{-0.03t} \\\\\\ \textit{again, we take \underline{ln} to both sides} \\\\\\ ln\left( \frac{3}{5} \right)=ln(e^{-0.03t})\implies ln\left( \frac{3}{5} \right)=-0.03t \\\\\\ \cfrac{ln\left( \frac{3}{5} \right)}{-0.03}=t\implies 17.0275\approx t[/tex]
so.. roughly about 17 days.
A building is 60 ft tall and another is 80 ft tall. A model of the 60 ft building is made at 1 ft. tall. How tall is the model of the 80 ft tall building?
Answers
1 foot = 60 feet
80/60 = 1.333
80 foot building is made 1.33 feet tall (16 inches, 1 foot 4 inches)
(04.01 LC)
Which of the tables represents a function?
Table A
Input
Output
3 1
3 4
2 3
Table B
Input
Output
2 7
5 6
2 9
Table C
Input
Output
1 5
7 2
7 3
Table D
Input
Output
3 4
1 5
8 5
Table A
Table B
Table C
Table D
Answers
Answer:
I believe the answer is table D.
Step-by-step explanation:
Each input can only have one output. The other tables have multiple outputs for each input. Therefore they get "cut off," and table D is the answer.
Helper's Message:
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-ChocoChocoCho
simplify
27 2/3
----------
27 4/3
Answers
We can write it like this,
[tex]\frac{27\frac{2}{3}}{27\frac{4}{3}}[/tex]
Let's convert them to improper fractions,
[tex]=\frac{\frac{83}{3}}{\frac{85}{3}}[/tex]
Let's divide them, but to do that we have to take the reciprocal of the second fraction,
[tex]=\frac{83\cdot \:3}{3\cdot \:85}[/tex]
Since our common factor is 3, we can cancel them out.
[tex]=\frac{83}{85}[/tex]
That would be our final answer.
Thanks
-TetraFish
Answer:
It would be 9
Step-by-step explanation:
for edgen 2020
the lines shown below are parallel. if the green line has a slope of -1/11, what is the slope of the red line?
a)-1/11
b)1/11
c)-11
d)11
Answers
Answer:
-1/11
Step-by-step explanation:
I just did it
Find the least common multiple of these two expressions. 14x^2y^4 and 21x^3u^7y^8
Answers
14 = 2 * 7
21 = 3*7
LCM = 2*3*7 = 42
answer is 42x^3u^7y^8
A customer calls and says that they are upset because they just received their bill and it is for two months service plus a $20 late fee. They have never had a late payment before. They explain that they moved last month and never received their bill. What would you tell them?
Answers
Answer with explanation:
The Customer , is irked due to the reason that,he or She hasn't got the last month bill and now they have to pay the bill for two months service plus $ 20 late fee.
Also, the customer is Saying that they moved from that place last month where they were Residing.
I will start Querying with the customer in the following way
Sir, or Madam
1. Have you checked , or asked your Neighbor or Landlord, after leaving that place ,whether they have got this kind of bill ?
2. Secondly , we have your email-ID as well as Mobile number.We message every month about your bill,through email as well as Messaging tool of your mobile.Haven't you Checked your Mail as well as Messaging.
it Shows that Customer is Lying.
So, Sir or Madam
Please , pay the Bill along with late fee.
Which of the following is an identity?
A. csc^2 x + cot^2 x = 1
B. (cscx + cotx)^2 = 1
C. sec^2 x sec^2 x + 1 = tan^2 x csc^2 x
D. sin^2 x - cos^2 x = 1
Answers
Nor D because sin^2 x + cos^2 x = 1
I think Its C
converting to sin's and cos's
1 / cos^4 x + 1 = sin^2 x / cos^2x * 1 / sin^2 x = 1 / cos^2 x
I dont think any are identities
You sure you have the question correct?
PLEASE PLEASE IM RUNNING OUT OF TIME AND NEED YOUR HELP!!!!!
hope i wrote these correctly!
Simplify: ^3√108c^17
My Choics are...
:
a. 6c^8√3c
b. 3^3√4c^17
c. 3c^5 ^3√4c^2
d. 18c^8√3c
Answers
answer
c. 3c^5 ∛4c^2
You flip a coin eight times. find the number of possible outcomes in the sample space.
Answers
The x-intercept of the line x = 3.5 is . The y-intercept of the line y = -6.5 is . Enter your answer as an ordered pair such as (1, 1) or (-2, 2).
Answers
Next, The y-intercept of the line y = -6.5 means that when x=0, and y=-6.5, so the order pair for this is (0,-6.5) or (0,-6 1/2). As a result, The x-intercept of the line x = 3.5 is (3.5,0) or (3 1/2,0) . The y-intercept of the line y = -6.5 is (0,-6.5) or (0,-6 1/2). Hope it help!
A ship traveled for 4 hours heading west and for 5 hours heading north. If the total distance traveled was 119 miles, and the ship traveled 5 miles per hour faster west, at what speed was the ship traveling west
Answers
then distance travelled west = time * speed = 4x
speed going North was x - 5 mph and distance = 5(x - 5)
so we have
4x + 5x -25 = 119
9x = 119+25 = 144
x = 144/9 = 16 mph <------ answer
A student claims that a figure has rotational symmetry and that the angle of rotational symmetry is 360 degrees. Critique the student's statement.
Answers
The graph of a line goes down and to the right when
Answers
In the polynomial below, what number should replace the question mark to produce a difference of squares? x2 + ?x - 49
Answers
(x + 7) (x-7) = 0
perform distribution and multiplication of terms such as shown below:
x² + 7x - 7x - 49 = 0
Combine the same term such as we can either add or subtract +7x to -7x and the result will be equal to 0x.
x² + 0x - 49 = 0
Therefore, the missing number is 0. The answer is 0 which will result to x² +0x - 49.
Answer:
0
Step-by-step explanation:
A veterinarian surveys her clients and finds that 32 percent of the households have dogs, 25 percent have cats, and 11 percent have both dogs and cats. Let event C be choosing a client who has cats and let event D be choosing a client who has dogs. Which statements are true? Check all that apply.
1.P(C | D) = 0.78
2.P(D | C) = 0.44
3.P(C ∩ D) = 0.11
4.P(C ∩ D) = P(D ∩ C)
5.P(C | D) = P(D | C)
Answers
let the total number of the clients be 100.
since there are 11 clients with both cats and dogs,
there are 32-11=21 clients with dogs but not cats
and 25-11=14 clients with cat but not dogs.
The number of clients with neither dogs nor cats is given by:
100-(21+11+14)=100-46=54
so we have the following:
P(C)=25/100=0.25
P(D)=32/100=0.32
P(C∩D)=P(D∩C)=11/100=0.11
we also have the formula P(A|B)=P(A∩B)/P(B), the formula of conditional probability
now we check each choice:
1. P(C|D)=P(C∩D)/P(D)=0.11/0.32=0.34
2. P(D|C)=P(D∩C)/P(C)=0.11/0.25=0.44
3 and 4 are already checked, and they are true
5. by 1 and 2, not true
Answer: 2, 3, 4 are True
The statements which are true based on the given sets of data are:
2.P(D | C) = 0.443.P(C ∩ D) = 0.114.P(C ∩ D) = P(D ∩ C)What is a Set?This refers to the grouping of data between different types of data within a range.
Based on the given information, we can see that
32% have dogs
25% have cats
11% has both cats and dogs
We can see that using a Venn diagram, we can make the graphical representation where there would be the intersection and Union of the data.
With this, we can see that options B, C and D are true because they satisfy the choosing events about the given set of data.
Read more about Venn diagram here:
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