Answer:
There are 2 options:
x = 32 cm and y = 62 cmx = 62 cm and y = 32 cmStep-by-step explanation:
That's a rectangular piece, therefore let's consider the width to be x and the length to be y.
A = width * length
1) A = x * y = 1,984 cm^2
P = 2 * (width) + 2 * (length)
2) P = 2x + 2y = 188 cm
Isolate x or y in one of the equations.
xy = 1,984 cm^2
y = 1,984 cm^2 / x
Now plug it in the second equation.
2x + 2y = 188 cm
2x + 2 * (1,984 / x) = 188
Now we have only one variable. Now just solve it alegebraically.
2x + (3,968 / x) = 188
Multiply both sides by x in order to get rid of the fraction.
[tex]2x^{2}[/tex] + 3968 = 188 x
Substract both sides by 188 x
2x^2 + 3968 - 188x = 0
Now divide by 2 to make the equation simpler.
x^2 - 94x + 1984 = 0
use the quadratic formula:
[tex]\frac{94 + \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 62\\\frac{94 - \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 32[/tex]
[tex]x1 = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \\x2 = \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
x is either 62 or 32.
let's find y:
y = 1,984 / x
y = 1,984 / 62 = 32
y = 1,984 / 32 = 62
There are 2 options:
x = 32 cm and y = 62 cmx = 62 cm and y = 32 cm
A group of students is writing a phone message app to provide better word suggestions based on the context of the word and the words the person used in the past. They will earn an A on the project if their teacher is convinced that their program suggests the correct word at least 54% of the time. The current success rate for this app is 54%. The teacher randomly selects 100 words and finds that the students’ program correctly suggests 64 of the words. To determine if this data provide convincing evidence that the proportion of correct words is more than 54%, 150 trials of a simulation are conducted. The results are shown in the dotplot. The teacher is testing the hypotheses: H0: p = 54% and Ha: p > 54%, where p = the true proportion of words the app will correctly predict. Based on the results of the simulation, what is the estimate of the P-value of the test?
Some pens are shared among three students anne,lucy, and John.Anne gets 5 times many pens as lucy, and lucy gets 2 pens less than john. Suppose John gets x pens, how many pens does anne get in terms of x
Using a system of equations, it is found that Anne gets 5x - 10 pens.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, we consider that John gets x pens.
Lucy gets 2 pens less than john, hence:
L = x - 2.
Anne gets 5 times many pens as lucy, hence:
A = 5L = 5(x - 2) = 5x - 10.
More can be learned about a system of equations at https://brainly.com/question/24342899
Given vectors
ā=(-1,-2), b=(-2,3), C = 3,-1),d =(-3,2)
find the dot product of b and c.
3
0-3
09
0-9
Answer:
-9
Step-by-step explanation:
b={-2,3)
c=(3,-1)
dot product b.c
=(-2×3) + (3×-1)
=-6+(-3)
=-6-3
=-9
If tomorrow i said, "the day before yesterday was saturday",then what is today?
Answer:
Monday
Step-by-step explanation:
If day before yesterday was Saturday, so today is Monday.
A doctor conducts a survey with a random sample of his patients, measuring their cholesterol levels in millimolar per liter.
The data measurements for 14 patients are given below. Assuming the population standard deviation is o = 1.3 and that
the population is normally distributed, compute a 90% confidence interval for the mean cholesterol levels of his patients.
Round your answers to two decimal places and use ascending order.
Using the z-distribution, as we have the standard deviation for the population, it is found that the 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.90[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.
Researching on the internet, the other parameters are given by:
[tex]\overline{x} = 6.16, \sigma = 1.3, n = 14[/tex]
Hence:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 6.16 - 1.645\frac{1.3}{\sqrt{14}} = 5.59[/tex]
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 6.16 + 1.645\frac{1.3}{\sqrt{14}} = 6.73[/tex]
The 90% confidence interval for the mean cholesterol levels of his patients is (5.59, 6.73).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Maya sells candles to her 5 neighbors. Each neighbor buys 2 boxes of candles. There are 6 candles in each box. What is the total number of candles that all of her neighbors will get?
A.
16 candles
B.
30 candles
C.
40 candles
D.
60 candles
Answer:
D. 60 Mark brainliest<3
Step-by-step explanation:
Each neighbor buys 2 boxes which contains 6 candles meaning they in total contain 12.
5x12 = 60
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answer:
Step-by-step explanation:
c) To find slope, choose any two points.
(2,16) & (4 , 31)
[tex]\boxed{slope= \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{31-16}{4-2}\\\\=\dfrac{15}{2}=7.5[/tex]
The slope is 7.5, which means that Kobby's puppy gained 7.5 pounds a month for the first 6 months.
a) Equation of line in slope -intercept form: y = mx +b
[tex]y =\dfrac{15}{2}x+b[/tex]
Now, substitute the point (2 ,16) in the above equaiton and find the y-intercept b.
[tex]\sf 16 =\dfrac{15}{2}*2+b\\\\16=15+b\\\\16-15=b[/tex]
b = 1
Equation of the line:
[tex]y=\dfrac{15}{2}x+1[/tex]
b) y-intercept = 1
The y-intercept is 1, which means that Kobby'spuppy weighed 1 pound at birth
The population of a city increased from 21,400 to 27,700 between 2007 and 2016. Find the change
of population per year if we assume the change was constant from 2007 and 2016.
Answer:
700
Step-by-step explanation:
2016 - 2007 = 9
27,700 - 21,400 = 6300
6300 / 9 = 700.
UNDERSTAND VOLUME
When water is poured from the graduated cylinder below into a rectangular
prism, the rectangular prism is completely filled.
How many 1-cm unit cubes can be packed into the rectangular prism with no gaps
or overlaps?
Answer____ 1-cm unit cubes
Explain your answer.
Check the picture below.
liquid always take the shape of the container that contains it, so 25 cm³ from a beaker or pitcher or a curvy pipe dumped into another container, will always have 25 cm³ as its volume.
In this case it went from the cylinder to a prism, same 25 cm³.
notice in the picture, the volume of a green cube with those dimensions is just 1 cm³.
In 8- 11 find the area of each parrelogram or rhombus
The areas of the two parallelograms are 105 square inches and 20.997 square yards, respectively.
How to determine the area of a parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides with equal length and two pairs of angles of equal measure. The area of the parallelogram (A), in square yards or square inches, equals the product of its base length (b), in yards, and its height (h), in yards.
The area of each parallelogram is determined afterwards:
Exercise 10A = (10.5 in) · (10 in)
A = 105 in²
Exercise 11A = (9 yd) · (2.333 yd)
A = 20.997 yd²
The areas of the two parallelograms are 105 square inches and 20.997 square yards, respectively. [tex]\blacksquare[/tex]
To learn more on parallelograms, we kindly invite to check this verified question: https://brainly.com/question/1563728
PLEASE HELP ASAP, BEST ANSWER GETS +50 POINTS AND BRAINLIEST
prove that if the center of a circle is equidistant from the sides of an inscribed triangle, then the triangle is equilateral?
Please answer with a picture/drawing/diagram, and statement and reasons for Brainliest! Thanks!
Answer:
if your using a 60,60,60 triangle ; the centers are the same.
The triangle's equilateral.
hope it helps!!!
Step-by-step explanation:
See attached
Hope this helps! :D
complete each statement based on the image below
Step-by-step explanation:
1) Angles opposite congruent sides in a triangle are congruent, so angle H is congruent to angle D.
2) For the same reason as the first problem, angle D is congruent to angle NSD.
3) Since sides opposite congruent angles in a triangle are congruent, segment AH is congruent to segment AS.
4) For the same reason as the third question, segment SA is congruent to segment SN.
Give an example of a well-stated research question that involves estimating a characteristic about the population of part-time students at your college.
Improve the following research question so that it is a well stated research question. Research Question: Do students work a lot of hours?
Answer:
1) what is the number of male part time students between the ages 15 - 19 years?
2) do students work more than 4 hours a day?
1. y= x+ 12 Y= -18
2. y = x — 10 y=-12
Answer:
1) x=-30 2) x=-2
Step-by-step explanation:
1) y=x+12.
Y= -18
x+12=-18
x=-18-12
x=-30
2) y=x-10
y= -12
x-10=-12
x=-12+10
x=-2
Natalie randomly answered the last three
true-or-false questions on her math quiz.
What is the probability that she got at least
two correct?
The probability that Natalie got at least two correct on the last three
true-or-false questions is 1/4.
What is the probability that Natalie got at least two correct?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The sample space is 2. The question is either correct or wrong.
The probability that Natalie got at least two correct = 1/2 x 1/2 = 1/4
To learn more about probability, please check: https://brainly.com/question/795909
which fraction is the biggest?
[tex] \frac{2}{3} [/tex]
[tex] \frac{4}{5} [/tex]
[tex] \frac{7}{8} [/tex]
3+(-7)×2-10÷(-5)
please step by step0
[tex]\left[3+(-7)\times 2\right] - \left[10 \div(-5)\right]\\\\=(3-14) +\left(10\times \dfrac 15\right)\\\\=-11+2\\\\=-9[/tex]
Larger is 32 ounces and sells for 2.99 and smaller is 18 ounce and sells for 1.59
What is the better buy
Divide price by size of each and compare the u it price:
2.99/32 = 0.0934 per ounce
1.59/18 = 0.0883 per ounce
The 18 ounce do $1.59 has a lower cost per ounce so is the better buy
PLEASE HELP BEFORE MIDNIGHT
Answer:
Step-by-step explanation:
Variance=0.0016
Standard deviation is the square root of variance.
sigma=sqrt(0.0016)=0.04
mean=0.9 inch
Calculating z for 0.936 inch
z = (0.936 - 0.9)/0.04
= 0.036/0.04
= 0.9
Using normal distribution table
P(x<=0.936 inch)
= P(0.9)
= 0.81594
P(x>0.936) + P(x<=0.936) = 1
P(x>0.936)
= 1 - P(x<=0.936)
= 1 - 0.81594
= 0.18406
= 0.1841
Solve | x + 6| - 7 = 8
A: x= -9 and x = -21
B: x = 9 and x = -9
C: x = -9 and x = 21
D: x = 9 and x = -21
Answer:
x = 9,-21
Step-by-step explanation:
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Cancel absolute sign and add plus-minus to 15:
[tex]\displaystyle \large{x+6=\pm 15}[/tex]
Transport 6 to subtract ±15:
[tex]\displaystyle \large{x=\pm 15-6}[/tex]
Consider:
[tex]\displaystyle \large{x= 15-6}[/tex] or [tex]\displaystyle \large{x = -15-6}[/tex]
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x = 9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Second Method
Given:
[tex]\displaystyle \large{|x+6|-7=8}[/tex]
Transport -7 to add 8:
[tex]\displaystyle \large{|x+6|=8+7}\\\displaystyle \large{|x+6|=15}[/tex]
Absolute Function Property:
[tex]\displaystyle \large{|x-a| = \begin{cases} x-a \ \ (x \geq a) \\ -x+a \ \ (x < a) \end{cases}}[/tex]
Consider both intervals:
When x ≥ a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{x+6=15}[/tex]
Transport 6 to subtract 15:
[tex]\displaystyle \large{x=15-6}\\\displaystyle \large{x=9}[/tex]
When x < a then:
[tex]\displaystyle \large{|x+6|=15}\\\displaystyle \large{-(x+6)=15}\\\displaystyle \large{-x-6=15}[/tex]
Transport -6 to add 15:
[tex]\displaystyle \large{-x=15+6}\\\displaystyle \large{-x=21}[/tex]
Transport negative sign to 21:
[tex]\displaystyle \large{x=-21}[/tex]
Solution:
[tex]\displaystyle \large{x=9}[/tex] or [tex]\displaystyle \large{x=-21}[/tex]
__________________________________________________________
Let me know if you have any questions regarding this question, my answer or explanation. Hope this answer and explanation helps you and good luck with your assignment!
The second term of a geometric progression is -576 and the fifth term is 243. Find:
a) the common ratio
b) the first term
c) the sum to infinity.
What is the range of f(x)?
What is the answer for B
Rosa invests $1100 in one account and $1300 in an account paying 3 % higher interest. At the end of one year she had earned $255 in interest. At what rates did she invest?
$1100 invested at __%
$1300 invested at __%
Answer:
$1100 at 9%$1300 at 12%Step-by-step explanation:
The amount of interest earned in one year is the product of the interest rate and the amount invested at that rate. The total interest earned is the sum of the amounts of interest earned on each investment.
Let x represent the lower interest rate. Then the higher rate is x+0.03 and the total interest earned is ...
1100x +1300(x+0.03) = 255
2400x +39 = 255 . . . simplify
2400x = 216 . . . . . . subtract 39
x = 216/2400 = 0.09 = 9% . . . . divide by the coefficient of x
Rosa invested $1100 at 9%, and $1300 at 12%.
Solve (image attached)
Answer:
70 degrees
Step-by-step explanation:
We know that a straight line is 180 degrees so this equation can be used:
80 + x + 30 = 180
110 + x = 180
x = 70
Hope this helps :)
Answer:the largest angle has a measure of ____degrees.
NO LINKS!!
Part 2: Figure A is a dilated image of Figure B. Find the scale factor. #3 and 4
Answer:
Step-by-step explanation:
Take one side length
B=16unitsA=12unitsScale factor (A to B)
[tex]\\ \rm\rightarrowtail \dfrac{16}{12)=\dfrac{4}{3}[/tex]
Scale factor (B to A)=1/4/3=3/4
#4
B=4unitsA=8unitsScale factor (A to B)
4/8=1/2Scale factor (B to A)
2It is a widely held belief that a typical piece of printer paper with a thickness of 0.1 mm can go through at most 7 folds. When folding a piece of paper in half, the number of layers doubles with each fold, which also doubles the thickness. Sylvia is testing this theory and employing a hydraulic press in order to ensure each fold is as tight as possible. If Sylvia is successful in folding the paper completely, determine the thickness of her piece of printer paper after being folded in half 7 times.
12.8mm
Step-by-step explanation:[tex]0.1\times2^7\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\{2^7\right.=2\times2\times2\times2\times2\times2\times2\\ =0.1\times128\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\left.\ 128\right\}\\ =12.8mm[/tex]
I hope this helps you
:)
(WILL MARK BRAINLIEST) Keisha is playing a game using a wheel divided into 8 equal sectors, as shown in the diagram below. Each time the spinner lands on blue, she will win a prize.
If Keisha spins this wheel twice, what is the probability that she will win a prize on both spins?
Answer:
6/11
Each time you spin the pointer there is a 3/8 for each of the two spins. That means there is a 6/11 chance of the pointer landing on blue for both times the pointer is spun.
Step-by-step explanation:
Each spin there are 8 possible sections the spinner can land on. The circle has 3 blue sections. The question asks what is the probability of the spinner landing on blue for BOTH spins. This means that you would have to show the denominator as 16. Each time you spin the pointer there is a 3/8 chance it will touch blue. When you spin it two times there is a 6/16 probability that the spinner will land on blue for each of the times the pointer is spun.
Have a great rest of your day
#TheWizzer
Which symbol < > = will make the comparison true 4/6 and 4/8
Answer:
4/6 > 4/8
Step-by-step explanation:
To see if the following is true:
We can cross multiply:
[tex]\frac{4}{6}\neq \frac{4}{8}[/tex] {4* 8 = 32} {4*6=24}
Thus,
[tex]\frac{4}{6}=32[/tex]
[tex]\frac{4}{8}=24[/tex]
Hence, [tex]\frac{4}{6} > \frac{4}{8}[/tex]
We can also turn them into decimal:
[tex]\frac{4}6=0.6667[/tex]
[tex]\frac{4}{8}=0.5[/tex]
0.5 is NOT greater than 0.6667 which also means that 4/8 is NOT greater than 4/6.
~lenvy~