Recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length. The length of a rectangle is 2 times the width. If the area is 392 square feet, then what is the length of the rectangle, in feet?
Answer:
7.7
Step-by-step explanation:
I did it on edu!
You can use the fact that area of a rectangle is its length times its width.
The length of the given rectangle is 28 feet.
What is the area of a rectangle?Area of a rectangle is its length times its width.
If a rectangle has length x units and width y units, then we have:
[tex]Area = x \times y \: \rm unit^2[/tex]
How to calculate the values of items which are not known?Most of the times, you will get some other facts or information by which the unknown values of those items can be known. For simple daily life cases, we can use variables, which are nothing but just placeholders for those unknown values. We can then operate on those variables assuming them to be actual values, thus, getting near to their original values.
Using above method for getting the length of the rectangleLet the length of the given rectangle be x units, and let its width be y
Then as it is given that
Length of the rectangle = 2 times width of the rectangle
or
[tex]x = 2 \times y[/tex]
We have area= 392 square feet
Since area = length times width, thus, we have
[tex]Area = x \times y\\392 = 2 \times y \times y\\\\\dfrac{392}{2} = y^2\\\\y^2 = 186\\\\\text{\:(Taking positive root on both the sides since y is width, a non negative quantity)}\\\\y = \sqrt{196} = 14[/tex]
Thus, the width of the rectangle is 14 feet
And thus, the length of the rectangle = double of width = 28 feet.
Thus,
The length of the given rectangle is 28 feet.
Learn more about area of rectangle here:
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the square of a number plus three times the number is 70. find the numbers.
Answer:
Step-by-step explanation:
The equation for that is
[tex]x^2+3x=70[/tex]
If we subtract over the 70, we have a quadratic that we can factor to solve for the values of x that will make that equation true.
[tex]x^2+3x-70=0[/tex]
Now we need the factors of 70 that will either add or subtract to give us the linear term of 3. The factors of 70 that will work are 10 and 7. 10 times 7 is 70, and 10 - 7 = 3:
[tex]x^2+10x-7x-70=0[/tex] and now we will factor by grouping:
[tex](x^2+10x)-(7x-70)=0[/tex] and factor out what's common:
[tex]x(x+10)-7(x+10)=0[/tex]
The factor (x + 10) is common, so we will now factor that out:
[tex](x+10)(x-7)=0[/tex]
By the Zero Product Property, either x + 10 = 0 or x - 7 = 0, so x = -10 or 7
Those are the 2 numbers that will work.
[tex](-10)^2+3(-10)=70[/tex] simplifies to
100 - 30 which does in fact equal 70. OR
[tex](7)^2+3(7)=70[/tex] which simplifies to
49 + 21 which also equals 70.
So you're done!
The values of the unknown number is 7 or - 10
The given expression from words to algebra;
let the unknown number = n
the square of the number = n²
three times the number = 3n
n² + 3n = 70
To find:
the values of nThe values of n is calculated as follows;
[tex]n^2 + 3n = 70\\\\n^2 + 3n - 70 = 0\\\\factorize \ the \ equation;\\\\n^2 + 10n - 7n - 70 = 0\\\\n(n + 10) - 7(n + 10) = 0\\\\(n-7)(n+ 10) = 0\\\\n = 7 \ or \ - 10[/tex]
Thus, the values of the unknown number is 7 or - 10
Learn more here: https://brainly.com/question/16889590
How tall would the lighthouse be?...
Answer:
122.6 m
Step-by-step explanation:
Shadow cast by the man = 3.1 m
Height of the man = 1.9 m
Shadow cast by the lighthouse = 200 m
Height of the lighthouse = x
If two shapes are similar, the ratio of their corresponding sides would be equal.
Therefore,
x/1.9 = 200/3.1
Multiply both sides by 1.9
x = (200*1.9)/3.1
x = 122.6 m (nearest tenth)
The lighthouse is 122.6 m tall
Jorge has some dimes and quarters. He has 10 more dimes than quarters and the collection of coins is worth $2.40. How many dimes and quarters does Jorge have?
Answer:
14 dimes and 4 quarters
Step-by-step explanation:
x= number of dimes
y=number of quarters
x-10=y
0.10x+0.25y=2.40
substitute for y
0.10x+0.25(x-10)=2.40
0.35x-2.50=2.40
0.35x=4.90
x=14
y=4
Help I don’t know the answer
Answer:
the last one
Step-by-step explanation:
the input cannot be negative
the difference of two numbers is 15. the larger number is 1 more than 3 times the smaller number. find the two numbers.
Answer:
7, 22
Step-by-step explanation:
3!=6+6=12/3=4!=24-4=20-10=10-3=7
11-1=10+2=12/6=2x11=22
Shanti began to draw a Venn diagram comparing refracting and reflecting telescopes.
2 overlapping circles. The left circle labeled Refracting telescopes. The right circle labeled Reflecting Telescopes. An X in the overlap. Both as a label below and outside the overlap.
Which label could be written in the area marked X?
“Uses a convex mirror”
“Uses a concave mirror”
“Uses a concave eyepiece lens”
“Uses a convex eyepiece lens”
Answer:
D im pretty sure. "Uses a convex eyepiece lens”
Step-by-step explanation:
I am taking quiz rn
The correct label that could be written in the area marked X is "Uses a convex eyepiece lens".
What is the Venn diagram?The Venn diagram is a mathematical representation of the system of scenarios.
Here,
The overlapping area between the two circles represents the features that both types of telescopes share. Reflecting telescopes use concave eyepiece lenses the primary optical element while refracting telescopes use a convex eyepiece lens. So the X in the overlapping area represents the fact that there are some telescopes that “Use a convex eyepiece lens".
A concave mirror is used in reflecting telescopes to collect and focus light, while a convex eyepiece lens is used to magnify the image. The other two options ("Uses a convex mirror" and "Uses a concave mirror") are not accurate for both types of telescopes.
Learn more about Venn diagrams here:
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#SPJ6
please help i’m so confused, it’s geometry!
Answer:
The correct answer is (-1,-3)
Step-by-step explanation:
its right i think lol
When a teacher counted her students in groups of 4, there were two students left over. When she counted them in groups of 5, she had 1 student left over. If 15 of her students were girls and she had more girls than boys, how many students did she have?
Steve manages a skate park and he has been analyzing the attendance data. Steve finds that the number of visitors increases exponentially as the temperature increases, and this situation is represented by the function f(x) = 5x. Steve also finds a linear equation that models the number of people who leave the park early depending on the change in temperature, and it is represented by f(x) = −x + 6. The graph of the two functions is below. Find the solution to the two functions and explain what the solution represents. (10 points)
Answer:
(1, 5)Step-by-step explanation:
Both of the graphs include infinite number of points.
The solution is the common point that belongs to both of the graphs, the intersection point.
We can see it is the point (1, 5)
This is the point when the temperature change is positive 1 degree. At this point number of visitors is equal to number of those leaving the part early.
If p:q=2/3:3 and p:r=3/4:1/2, calculate the ratio p:q:r
Can someone help me with this math question?...
Answer:
B.
Step-by-step explanation:
It is the right answer, I promise.
Answer:
It is B. Length = 22 Feet, Width = 20 Feet
Step-by-step explanation:
I got it right once
Helppp again plzzzzzzzhsjsjskzkzjdosoa
Answer:
1
Step-by-step explanation:
-16 + x = -15
+16 +16
x = 1 because -15 + 16 is 1
find the value of x for the following equation 4(6x -9.5) = 46
Step-by-step explanation:
step 1. 24x - 38 = 46 (distributive property)
step 2. 24x = 84 (add 38 to both sides)
step 3. x = 84/24 = 21/6 = 7/2 (divide by 24 and simplify).
The sum of two numbers is 23. The sum of the smaller and 2 times the larger is 36. Find the numbers.
Answer
How to enter your answer
larger number:
smaller number:
5. If the covariance between the variables x and y is 18 and the variance
of x and y are 16 and 81 respectively. Find the coefficient of
correlation.
Answer:
The coefficient of correlation=0.5
Step-by-step explanation:
We are given that
Covariance between the variable x and y=18
Variance of x=16
Variance of y=81
We have to find the coefficient of correlation
We know that
Coefficient of correlation
[tex]r=\frac{covariance(x,y)}{\sqrt{variance(x)}\times \sqrt{variance(y)}}[/tex]
Using the formula
[tex]r=\frac{18}{\sqrt{16}\times \sqrt{81}}[/tex]
[tex]r=\frac{18}{4\times 9}[/tex]
[tex]r=0.5[/tex]
Hence, the coefficient of correlation=0.5
$6,000 at 6%
for 8 years
What is the amount of interest earned
Answer:
13,243
Step-by-step explanation:
hope this helps
i am bad at math
Can You please help me
9514 1404 393
Answer:
S > 2
Step-by-step explanation:
In this context, "over" means "greater than." The problem statement tells you the weight (S) is greater than 2 kilograms:
S > 2
PLEASE HELP! Which of the following expressions are equivalent to (x+y) - (-z)?
A) (x+y)-z
B)x+(y+z)
C) none of the above
Answer:
c
Step-by-step explanation:
none of them equal (x+y)-(-z)
The formula is T = L/S, where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. How long a tape does a police officer need to record a 2-minute confession at an operating speed of 3 1/2 inches per second?
Answer:
im not sure im sorry
Step-by-step explanation:
not sure
Amphibian populations are in decline worldwide due to the increasing prevalence of ranavirus infections. Herpetologists (those that study amphibians and reptiles) are especially concerned with how ranavirus infections may be affecting Ozark and eastern hellbender populations.
Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%. Suppose a random sample of size 118 is taken of the eastern hellbender population and a random sample of size 177 is taken of the Ozark hellbender population. Every hellbender in each sample is tested for ranavirus, and the sample proportions for each of the two samples are calculated.
Required:
Which of the two sample proportions is more likely to exceed 22% ?
Answer:
The sample proportion of size 177 is more likely to exceed 22%.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%.
This means that [tex]\mu = p = 0.25[/tex]
Sample of size 118:
[tex]n = 118, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0399[/tex]
Probability of sample proportion above 22%.
This is 1 subtracted by the pvalue of Z when X = 0.22. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.25}{0.0399}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a pvalue of 0.2266
1 - 0.2266 = 0.7734
0.7734% probability that a random sample of size 118 exceeds 22%.
Sample of size 177:
[tex]n = 177, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0325[/tex]
Probability of sample proportion above 22%.
This is 1 subtracted by the pvalue of Z when X = 0.22. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.25}{0.0325}[/tex]
[tex]Z = -0.92[/tex]
[tex]Z = -0.92[/tex] has a pvalue of 0.1788
1 - 0.1788 = 0.8212
0.8212 = 82.12% probability that a random sample of size 177 exceeds 22%.
82.12% > 77.34%, so the sample proportion of size 177 is more likely to exceed 22%.
The sample proportion that is more likely to exceed 22% is; the sample proportion with a sample size of 177
Central Limit Theorem
We are given;
Population proportion; p = 25% = 0.25
Now, in central limit theorem, the formula for standard deviation is;
σ = √(p(1 - p)/n)
For a sample size of 118, we have;
σ = √(0.25(1 - 0.25)/118)
σ = √0.001588983
σ = 0.03986
Similarly, for a sample size of 177, we have;
σ = √(0.25(1 - 0.25)/177)
σ = √0.001059322
σ = 0.032547
Since we want to find which of the two sample proportions will likely exceed 22% which is p₀ = 0.2, we will use the formula;
z = (p₀ - p)/σ
For sample size of 118, we have;
z = (0.22 - 0.25)/0.03986
z = -0.75
From online p-value from z-score calculator, we have;
p-value = 0.7734 or 77.34%
For sample size of 177, we have;
z = (0.22 - 0.25)/0.032547
z = -0.92
From online p-value from z-score calculator, we have;
p-value = 0.8212 or 82.12%
The p-value of the sample of 177 is higher than the p-value for the sample of 118 and so we can say that the sample proportion with a sample size of 177 is more likely to exceed 22%
Read more about Central Limit theorem at; https://brainly.com/question/25800303
Find the slope of the line that passes through the two points.
Answer:
slope is 5
Step-by-step explanation:
use formula (y2-y1)/(x2-x1) to find the slope
(2-(-3))/(6-5)
= 5/1
=5
if you want the equation to the graph here:
y=mx+b
2=5(2)+b
2=10+b
b=-8
equation: y=5x-8
Help please being timed and I don’t get it...?
Answer:
i got you.
whats up
Step-by-step explanation:
Review the work showing the first few steps in writing a partial fraction decomposition.
StartFraction 2 x squared + 15 x + 19 Over (x + 4) cubed EndFraction = StartFraction A Over x + 4 EndFraction + StartFraction B Over (x + 4) squared + StartFraction C Over (x + 4) cubed EndFraction
2x2 + 15x + 19 = A(x + 4)2 + B(x + 4) + C
2x2 + 15x + 19 = Ax2 + 8Ax + 16A + Bx + 4B + C
Which system of equations can be used to determine the values of A, B, and C?
Answer:
[tex]A = 2[/tex]
[tex]B = -1[/tex]
[tex]C = -9[/tex]
Step-by-step explanation:
Given
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
Required
Find A, B and C
Rearrange the expression
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + 16A + Bx + 4B + C[/tex]
[tex]2x\² + 15x + 19 = Ax\² + 8Ax + Bx + 16A + 4B + C[/tex]
To do this, we simply compare the expressions on both sides of the equation.
So, we have:
[tex]Ax\² = 2x\²[/tex] --- (1)
[tex]8Ax + Bx = 15x[/tex] --- (2)
[tex]16A + 4B + C = 19[/tex] --- (3)
Divide both sides by x² in (1)
[tex]Ax\² = 2x\²[/tex]
[tex]A = 2[/tex]
Divide both sides by x in (2)
[tex]8Ax + Bx = 15x[/tex]
[tex]8A + B = 15[/tex]
Substitute 2 for A.
[tex]8*2 + B = 15[/tex]
[tex]16+ B = 15[/tex]
Make B the subject
[tex]B = 15 - 16[/tex]
[tex]B = -1[/tex]
Substitute 2 for A and -1 for B in (3)
[tex]16A + 4B + C = 19[/tex]
[tex]16*2 + 4*-1 + C = 19[/tex]
[tex]32 - 4 + C = 19[/tex]
[tex]28 + C = 19[/tex]
Make C the subject
[tex]C = 19 - 28[/tex]
[tex]C = -9[/tex]
Answer:
it D
Step-by-step explanation:
I just used elimination like a small brain
like so
when a = 1, b = 0, c = 3, d = -3
x^3 + 8x – 3 = Ax^3 + 5Ax + Bx^2 + 5B + Cx + D
What is 22.5% written as a fraction in simplest form?
Answer:
9/40
Step-by-step explanation:
Write down the percent divided by 100 like this:22.5/100
Multiply both top and bottom by 10 for every number after the decimal point:As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,(22.5*10)(100*10)= 225/1000
Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25.225 ÷ 25/ 1000÷25 = 9/40
factor the expression by grouping: ax+ay+az+3x+3y+3z
please answer fast
Answer:
(x+y+z)(a+3)
Step-by-step explanation:
ax+ay+az+3x+3y+3z
=(ax+ay+az)+(3x+3y+3z)
=a(x+y+z)+3(x+y+z)
=(x+y+z)(a+3)
How many ways are there to add three positive even numbers to get a sum of 20? Solve this
problem by making a systematic list, then state your solution.
Help!!!!! can you show your work too thanks
Answer:
no entender veri mucho......aaaa
11.3
Example 3: A person randomly selects one of the four envelopes
shown below. Each envelope contains a check that the person gets
to keep. However, before the person can select the envelope, he or
she must pay $7 to play. Determine the person's expectation for the
following:
Answer:
Mathematical expectation is to get %280%2B3%2B7%2B22%29%2F4 = 32%2F4 = 8 dollars from the envelopes.
Statistically, it is loosing game.Step-by-step explanation:
Which students reads the faster rate in your final answer include all necessary calculations
Answer:
Connie
Step-by-step explanation:
Determine the reading rate of the three students each. The student with the highest number of pages per minute is the fastest student (i.e. reads more words per minute).
✔️Stew's Reading Rate:
2650 ÷ 10 = 265 words per minute
✔️Connie's Reading Rate:
From the graph, it shows that 200 words are read in 1 minute.
So we have, 200 words per minute.
✔️Felicia = 260 words per minute
Therefore, we can conclude that Connie is the fastest because Connie reads more words per minute, which is 265 words per minute. Connie reads at a faster rate.
Question 1 of 10
Which of the following is equal to the fraction below?
N
(17)"
A. 711
N
B.
44
C. 11.
11.6)
1
D. 711
Answer:
i feel like the answer is d srry if im wrong
Step-by-step explanation: