Answer: The length is 4 centimeters and the width is 6 centimeters.
Step-by-step explanation:
If the length of the rectangle is eight centimeters less than twice the width then we could represent it by the equation L= 2w - 8 . And we know that to find the area of a rectangle we multiply the length by the width and they've already given the area so we will represent the width by w since it is unknown.
Now we know the length is 2w- 8 and the width is w so we would multiply them and set them equal to 24.
w(2w-8) = 24
2[tex]w^{2}[/tex] - 8w = 24 subtract 24 from both sides to set the whole equation equal zero and solve. solve using any method. I will solve by factoring.
2[tex]w^{2}[/tex] - 8w -24 = 0 divide each term by 2.
[tex]w^{2}[/tex] - 4w - 12 = 0 Five two numbers that multiply to get -12 and to -4
[tex]w^{2}[/tex] +2w - 6w - 12 = 0 Group the left hand side and factor.
w(w+2) -6( w + 2) = 0 factor out w+2
(w+2)(w-6) = 0 Set them both equal zero.
w + 2 =0 or w - 6 = 0
-2 -2 + 6 +6
w= -2 or w=6
Since we are dealing with distance -2 can't represent a distance so the wide has to 6.
Now it says that the length is 8 less that twice the width.
So 2(6) - 8 = 12 -8 = 4 So the length in this care is 4.
Check.
6 * 4 = 24
24 = 24
I WILL RATE YOUR BRAINLIEST Marius opened a savings account. The sequence {200, 208, 216.30, 225, …} describes the amount of interest he earns each year his account is active. If this pattern continues, how much total interest will Marius have earned by the 30th year the account is active?
Answer:
11,215Step-by-step explanation:
Given the sequence of interest earned by Marius on his savings account as
200, 208, 216.30, 225, …, the sequence of interest forms a geometric sequence since they have a common ratio.
[tex]r =\frac{T_2}{T_1}= \frac{T_3}{T_2}= \frac{T_4}{T_3}\\ r =\frac{208}{200}= \frac{216.30}{208}= \frac{225}{216.30} \approx 1.04[/tex]
To get how much total interest will Marius have earned by the 30th year the account is active, we will find the sum of the first 30 terms of the geometric sequence as shown.
[tex]S_n =\frac{ a(r^n-1)}{r-1} \ for \ r> 1\\ \\\\ n = 30, a = 200, r = 1.04\\S_{30} = \dfrac{ 200(1.04^{30}-1)}{1.04-1}\\\\S_{30} = \dfrac{ 200(3.243-1)}{0.04}\\\\S_{30} = \dfrac{ 200(2.243)}{0.04}\\\\S_{30} = \dfrac{ 448.6}{0.04}]\\\\S_{30} = 11,215[/tex]
Hence total interest that Marius will earn by the 30th year the account is active is 11,215.
the correct answer is
S30= 200(1-1.04^n)/1-1.04
i took the test
Translate verbal expression to an algebraic expression
8 times a number x is subtracted by 4
Answer:
8x - 4
Step-by-step explanation:
8x - 4
Translated algebraically expression is 8x-4
What is expression?
Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given verbal expression that,
8 times a number x is subtracted by 4
(1) Let x = the unknown number.
(2) "8 times a number of x" is translated algebraically as 8x
(3) "same number x is subtracted by 4" is translated algebraically as 8x -4
Putting analyses together translated algebraically into the following equation as the result : 8x-4
Learn more about algebraic expressions
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A researcher is interested in finding a 90% confidence interval for the mean number of times per
day that college students text. The study included 147 students who averaged 44.7 texts per
day. The standard deviation was 17.9 texts. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a tv distribution.
b. With 90% confidence the population mean number of texts per day is between
and
texts.
Answer:
90% confidence the Population mean number of texts per day
(42.2561 ,47.1439)
Step-by-step explanation:
Step(i):-
Given sample size 'n' = 147
mean of the sample size x⁻ = 44.7
standard deviation of the sample 'S' = 17.9
90% confidence the Population mean number of texts per day
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
Step(ii):-
Degrees of freedom
ν=n-1=147-1=146
t₀.₁₀ = 1.6554
[tex](x^{-} - t_{\alpha } \frac{S}{\sqrt{n} } ,(x^{-} + t_{\alpha } \frac{S}{\sqrt{n} })[/tex]
[tex](44.7 - 1.6554 \frac{17.9}{\sqrt{147} } ,(44.7 + 1.6554 \frac{17.9}{\sqrt{147} })[/tex]
(44.7 - 2.4439 ,44.7 + 2.4439 )
(42.2561 ,47.1439)
Conclusion:-
90% confidence the Population mean number of texts per day
(42.2561 ,47.1439)
Find a polar equation r for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)
Conic: Parabola Eccentricity: e = 1 Directrix: y = 4
Answer:
The equation is [tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
Step-by-step explanation:
From the equation we are told that
The Eccentricity: e = 1
The Directrix is y = 4
Generally the polar equation for e = 1 and y = + c is mathematically represented as
[tex]r = \frac{e * c }{ 1 + ecos (\theta )}[/tex]
So
[tex]r = \frac{1 * 4 }{ 1 + 1 * cos (\theta )}[/tex]
[tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of ^{14}\text{C} 14 C. Estimate the minimum age of the charcoal, noting that
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] . Estimate the minimum age of the charcoal, noting that [tex]2^{10} = 1024[/tex]
Answer:
57300 years
Step-by-step explanation:
Using the relation of an half-life time in relation to fraction which can be expressed as:
[tex]\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}[/tex]
here;
N represents the present atom
[tex]N_o[/tex] represents the initial atom
t represents the time
[tex]t_{1/2}[/tex] represents the half - life
Given that:
Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] .
Then ;
[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]
However; we are to estimate the minimum age of the charcoal, noting that [tex]2^{10} = 1024[/tex]
so noting that [tex]2^{10} = 1024[/tex], then:
[tex]\dfrac{1}{1000}> \dfrac{1}{1024}[/tex]
[tex]\dfrac{1}{1000}> \dfrac{1}{2^{10}}[/tex]
[tex]\dfrac{1}{1000}> (\dfrac{1}{2})^{10}[/tex]
If
[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]
Then
[tex]\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}[/tex]
Therefore, the estimate of the minimum time needed is 10 half-life time.
For [tex]^{14}\text{C}[/tex] , the normal half-life time = 5730 years
As such , the estimate of the minimum age of the charcoal = 5730 years × 10
= 57300 years
Students who score within 14 points of the number 88 will pass a particular test. Write this statement using absolute value notation and use the variable x for the score.
Answer:
|88-x| ≤ 14
Step-by-step explanation:
their score has to be within 14 points of 88.
if their score is above 88, the number will be negative, but the absolute value makes the number positive. if that number is still within 14 of 88, they pass.
if their score is below 88, the number will be negative, and the absolute value keeps the number positive. if that number is still within 14 of 88, they pass.
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answer:
154.2
Step-by-step explanation:
To find the average of the bowlers scores, you have to find the mean by adding the values and dividing by the number of values.
To find the bowlers average add the scores and divide by the number of games.
143+156+172+133+167/5=154.2 is the average score for the bowler.
)Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profit
percentage. Show your working.
Answer:
40.60-35=5.6
Step-by-step explanation:
Profit is cost minus the amount you sold it for
Use technology to solve the following problem: A certain car model has a mean gas mileage of 30 miles per gallon (mpg) with a standard deviation A pizza delivery company buys 42 of these cars. What is the probability that the average mileage of the fleet is greater than
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, let me solve a question that is exactly like this one.
A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?
Answer:
Given that the mean (μ) is 34 miles per gallon (mpg) with a standard deviation (σ) 5 mpg. The sample (n) is 43.
The z score is used in statistics to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\for\ a \ sample\ size:\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For the average mileage of the fleet is greater than 33.5 mpg (x > 33.5):
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\z=\frac{33.5-34}{5/\sqrt{43} } =-0.66[/tex]
From the normal distribution table, The probability that the average mileage of the fleet is greater than 33.5 mpg = P(x > 33.5) = P(z > -0.66) = 1 - P(z < -0.66) = 1 - 0.2546 = 0.7454 = 74.54%
8÷2(2+2)=?
I asked a few people some say it’s 1 and some say 16....
Answer:
16
Step-by-step explanation:
Follow the rules of PEMDAS
8÷2(2+2)
Parentheses
8÷2(4)
Exponents
we have none
Multiply and Divide from left to right
4(4)
16
Then Add and Subtract from left to right
Answer:
16
Step-by-step explanation:
In order to understand the answer to the problem, we need to know the correct order of operations, through the acronym PEMDAS
PEMDAS
P: Parentheses
E: Exponent
M: Multiply
D: Divide
A: Add
S: Subtract
First add everything in the parentheses to get 4
Then divide 8 by 2 to get 4
4 times 4 = 16
8/2= 4
2+2=4
4 x 4 = 16
In a survey of 200 publicly-traded companies, the average price-earnings ratio was 18.5 with a standard deviation of 8.2. When testing the hypothesis (at the 5% level of significance) that the average price-earnings ratio has increased from the past value of 16.8, the null and alternative hypotheses would be:________
Answer:
Null Hypothesis: H0:μ ≤ 16.8
Alternative Hypothesis: Ha: μ > 16.8
Step-by-step explanation:
We are told that affer testing the hypothesis (at the 5% level of significance), that the average price-earnings ratio increased from the past value of 16.8.
It means that the past value was not more than 16.8.
This follows that the null hypothesis is given as;
H0:μ ≤ 16.8
And since it has been discovered that the ratio increased from the past value of 16.8, the alternative hypothesis is;
Ha: μ > 16.8
WHY CAN'T ANYONE HELP ME PLEASE?A 40% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
40% solution = 20 gallons
80% solution = 60 gallons
Step-by-step explanation:
x = gallons of 40% solution
y = gallons of 80% solution
Total volume is:
x + y = 80
Total amount of fertilizer is:
0.40 x + 0.80 y = 0.70 (80)
Solve by substitution.
0.40 x + 0.80 (80 − x) = 0.70 (80)
0.40 x + 64 − 0.80 x = 56
0.40 x = 8
x = 20
y = 60
I need help with these questions asap, I will post pictures if you know them all answer them in the order of the photos from 1-5 thank you.
Answer:
1. step 4
2.idk
3. step 2
4.-5n = 1 ---------> n= -1/5
n + 15 = -10 -------> -25
n/5 = -1/5 ------> n = -1
n - 13 = -12 ------> n = 1
5. cant see the drop down menu or possible answers
but if an answer is the addition one thing
then the second one is the subtraction thing
Step-by-step explanation:
C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch. Calculate the Cpk for this machine.
Answer:
0.3333
Step-by-step explanation:
Given the following :
Sample mean(m) = 4.001 inch
Standard deviation(sd) = 0.002 inch
Key specification : = 4 ± .003 inches
Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches
Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches
Cpk is found using the relation:
min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]
min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]
min[(0.002 / 0.006), (0.004 / 0.006)]
min[(0.33333, 0.66667)
Therefore Cpk = 0.3333
Because 0.33333<0.66667
Use the information provided to determine a 95% confidence interval for the population variance. A researcher was interested in the variability in service time (in hours) spent by mechanics fixing the same automotive problem. A random sample was taken resulting in a sample of size 20 from a substantial file of reported experience. The summary statistics are as follows: n = 20, sample mean = 13.8 hours, sample standard deviation = 3.9 hours. Assume service time follows a normal distribution. Round to two decimal places.
Answer:
The 95% confidence interval for the population variance is (8.80, 32.45).
Step-by-step explanation:
The (1 - α)% confidence interval for the population variance is given as follows:
[tex]\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
It is provided that:
n = 20
s = 3.9
Confidence level = 95%
⇒ α = 0.05
Compute the critical values of Chi-square:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2, (20-1)}=\chi^{2}_{0.025,19}=32.852\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.05/2, (20-1)}=\chi^{2}_{0.975,19}=8.907[/tex]
*Use a Chi-square table.
Compute the 95% confidence interval for the population variance as follows:
[tex]\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}[/tex]
[tex]\frac{(20-1)\cdot (3.9)^{2}}{32.852}\leq \sigma^{2}\leq \frac{(20-1)\cdot (3.9)^{2}}{8.907}\\\\8.7967\leq \sigma^{2}\leq 32.4453\\\\8.80\leq \sigma^{2}\leq 32.45[/tex]
Thus, the 95% confidence interval for the population variance is (8.80, 32.45).
Is y = 8x -15 a function?
Answer:
Hey there!
A function only has one y value for every x value, so this is a function. Additionally, all linear equations (that are in the y=mx+b form) are functions.
Hope this helps :)
Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?
Answer:
Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.
Step-by-step explanation:
Suppose we have events X and Y.
1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.
2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.
group the like term together
Answer:
Step-by-step explanation:
[tex]xy^{2}[/tex], [tex]5y^{2}x[/tex], [tex]\frac{-3}{5}[/tex][tex]xy^{2}[/tex]
[tex]-3x^{2}y[/tex], [tex]\frac{2}{3}[/tex][tex]yx^{2}[/tex]
Hope this helps
plz mark it as brainliest!!!!!
Consider these five values a population: 7, 4, 6, 4, and 7. Determine the mean of the population. (Round your answer to 1 decimal place.)
Answer:
[tex]Mean = 5.6[/tex]
Step-by-step explanation:
Given
[tex]7,4,6,4,7[/tex]
Required
Determine the mean
Mean is calculated as thus;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where n is the number of observation;
In this case;
[tex]n = 5[/tex]
and [tex]\sum x[/tex] is the sum of the observations
The expression becomes
[tex]Mean = \frac{7+4+6+4+7}{5}[/tex]
[tex]Mean = \frac{28}{5}[/tex]
[tex]Mean = 5.6[/tex]
Hence, the mean of the population is 5.6
determine the missing term x in the geometric sequence below
9,x,225
Answer:
45
Step-by-step explanation:
multiply 9 by 5 to get 45
then, multiply 45 by 5 to get 225
The geometric sequence is 5(previous number)
Which of the following is a correct factorization of this trinomial?
-4x² +11x-6
A. -(4x+3)(x + 2). B. -4(x+3)(x + 2)
C. -(x+3)(x-4)
D. (-4x+3)(x-2)
Answer:
D
Step-by-step explanation:
Step 1: Find the factors of 4 and -6
-4x² +11x-6
-4x 3
1x -2
(This works because -4 x -2 multiple to 8 and 3 x 1 gives you 3 and when you add it up it gives you the 'b' term)
Step 2: Read the numbers from left to right starting from the top to bottom
(-4x+3)(1x-2)
Therefore the answer to the question is D.
Answer:
A
explain
= -4x^2-11x-6
= -4x^2-8x-3x-6
= -4x(x+2)-3(x+2)
= (x+2) (-4x-3)
= -(4x+3) (x+2)
Time-series data are often graphically depicted how?
A. Bar chart.
B. Histogram.
C. Line chart.
D. All of these choices are true.
Answer:
C. Line chart
Step-by-step explanation:
Answer:
B. Histogram
Step-by-step explanation:
Histogram uses time.
Driver's Delight is considering building a new track. They have a circular space
with a diameter of 150 feet. Compute the circumference of the circular space.
Use 3.14 for it. Round your answer to the nearest hundredth, if necessary.
Answer:
The answer is 471 feetStep-by-step explanation:
Since the the track is circular
Circumference of a circle = πd
where
d is the diameter
π = 3.14
From the question
diameter = 150 feet
Circumference = 150π
= 150(3.14)
We have the final answer as
Circumference = 471 feetHope this helps you
Answer:
471.23 ft
Step-by-step explanation:
The circumference of this space is C = πd = (150 ft)π, or approximately
471.23 ft
1
Drag and drop the
labels to the correct
sides using Angle A
as a reference.
A
boy
3
4
hypotenuse
adjacent
opposite
5
6
hypotenuse goes to the line across from the right angle. adjacent is the bottom one. lastly opposite is the left one.
Step-by-step explanation:
Hi, there!!
According to the question, we should find the hypotenuse, adjacent, and opposite to the refrence angle A ,right.
so, let's simply work with it,
hypotenuse (h)= AC {side opposite to the 90° is always a hypotenuse}.
opposite (p)= BC { as the side opposite to the refrence angle is always perpendicular or opposite}
adjacent (b)= AB { as remaining side is always base or adjacent}
Hope it helps....
Solve for x if 2(1+3x)=14
Answer:
x=2
Step-by-step explanation:
2(1+3x)=14
Divide each side by 2
2/2(1+3x)=14/2
1+3x = 7
Subtract 1 from each side
3x =7-1
3x = 6
Divide by 3
3x/3 = 6/3
x =2
A+B = 20
B+C= 30
C+ A= 40
C =?
55 I hope this helps you!
I NEED this answered within the next 30 minutes! Please it is simple. There is an error in this. What is it?
Answer:
(a). x = 80°
(b). x = 7.2 units
Step-by-step explanation:
Angle formed between the tangents from a point outside the circle measure the half of the difference of intercepted arcs.
(a). Here the intercepted arcs are,
Measure of major arc = 360° - 100°
= 260°
Measure of minor arc = 100°
x° = [tex]\frac{1}{2}[m(\text{Major arc})-m(\text{Minor arc})][/tex]
= [tex]\frac{1}{2}(260-100)[/tex]
x = 80°
(b). If a secant and tangent are drawn form a point outside the circle, then square of the measure of tangent is equal to the product of the measures of the secant segment and and its external segment.
x² = 4(4 + 9)
x² = 4 × 13
x² = 52
x = √52
x = 7.211 ≈ 7.2 units
PLZ HELPPPPPP.
A store sells books for $12 each. In the proportional relationship between x, the number of books purchased, and y, the cost per books in dollars" to "y, the total cost of the books in dollars, the constant of proportionality is 12. Which equation shows the relationship between x and y?
A. y=12/x
B. y=12x
C. y=12+x
D. y=12−x
Answer:
B. y=12x
Step-by-step explanation:
x = # of books bought
so then y=12x
ASAP Which condition does not prove that two triangles are congruent? A. ASA ≅ ASA B. SAS ≅ SAS C. SSA ≅ SSA D. SSS ≅ SSS
Answer:
The answer is C. SSA ≅ SSA.
Step-by-step explanation:
To check for similar triangles, SSA congruence would not work because the other side can be any length. Also, there is not an SSA postulate because this theorem by itself cannot prove congruence.
The other three properties do work because they show congruence unlike the other congruent factors.
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot
Answer: 2*√18 + 3*√2 + √162 = 18*√2
Step-by-step explanation:
I guess that the equation is:
2*√18 + 3*√2 + √162
And we want to simplify it.
first 18 = 9*2
then we can write:
2*√18 = 2*√(9*2) = 2*3*√2 = 6*√2
and 162/9 = 18
then we can write:
√162 = √(9*18) = √9*√18 = 3√18
now we can use the previous step: √18 = 3*√2
and:
√162 = 3*(3*√2) = 9*√2
now we can write our equation as:
6√2 + 3√2 + 9√2 = (6 + 3 + 9)√2 = 18*√2
And now we can not simplify it further more, so here we end.
Answer:
B. 18 sqrt 2
Step-by-step explanation:
This is the correct letter and answer on edge, if thats what youre using:)
