The dimensions of the rectangle are, length = 5 inch and width = 6 inch.
What is rectangle?
A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.
Let, the length of a rectangle is 7 inches less than twice the width, w, of the rectangle.
Suppose,
width = w = x, then,
length = l = 2x - 7
Since the area of the rectangle is 30 square inches.
We know that.
Area of rectangle = length x width
30 = (2x - 7) x (x)
30 = 2x^2 - 7x
2x^2 - 7x - 30 = 0
2x^2 - 12x + 5x - 30 = 0
2x(x - 6) + 5(x - 6) = 0
(2x + 5)(x - 6) = 0
⇒ 2x + 5 = 0, x - 6 = 0
⇒ x = -5/2, x = 6
Since length is not negative.
Therefore, w = 6.
So, l = 2(6) - 7 = 12 - 7 = 5
Hence, the length is 5 inches and the width is 6 inches.
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Determine if they given ordered pair is a solution to the given system
Answer:
Step-by-step explanation:To determine if an ordered pair is a solution to a system of two equations, we substitute the values of the variables into each equation. If the ordered pair makes both equations true, it is a solution to the system.
A company claims that the mean weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randomly selected from a shipment indicated a mean weight of 122. 5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
The 95% confidence interval for the average apple weight is (119.14, 125.86).
An apple typically weighs 120 grams with a 12-gram standard deviation, according to one manufacturer. The average weight of an apple was 122. 5 grams, according to statistics created from a sample of 49 apples that were randomly chosen from a shipment.
Let, n = 49
x = 122.5
σ = 12
To calculate and interpret a 95% confidence interval for the average apple weight, use the formula;
⇒ (x ± 1.96*σ/√n)
⇒ (122.5 ± 1.96*12/√49)
⇒ (119.14, 125.86)
Consequently, the average apple weight has a 95% confidence interval of (119.14, 125.86).
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Suppose P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. What is
POV?
The P∩V is {2,4,6,8}.
From the question, we have
P= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
V= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
P∩V = {2,4,6,8}
Intersection of Sets:
The set that contains all the elements that are shared by two given sets is the intersection of the two sets. The intersection of sets is represented by the symbol "∩". The intersection A∩ B (also written as A intersection B) lists all the elements that are shared by any two sets A and B that are present in both sets.
For instance, if Set A = 1, 2, 3, 4, and Set B = 3, 4, 6, then A ∩B = {3,4}.
Complete question:
Suppose P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and V = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}. what is P ∩ V ?
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Carley cycled 72 miles in 3 hours. His cousin Catie drove 132
miles in 2 hours. Assume both cousins were driving at constant
speeds. How much faster was the faster person traveling?
Answer:
Speed at which Carley was cycling at
= 72 miles ÷ 3 hours
= 24 miles/hour
Speed at which Catie was driving at
= 132 miles ÷ 2 hours
= 66 miles/hour
66 miles/hour - 24 miles/hour = 42 miles/hour
∴ The faster person, Catie, was travelling 42 miles/hour faster than Carley, the slower person.
Gretta has a savings account with $6,500 in it that earns 9.5% simple interest per year. How much interest, to the nearest cent, will Gretta earn in 1 year? Give your answer in dollars.
Answer: $617.50
Step-by-step explanation:
9.5% of 6500 = 9.5*6500/100=9.5*65=617.5
So the interest is $617.5 or $617.50
Hope this helped. If you have any questions or clarifications please ask.
Thanks and please rate!
Answer:
Gretta will earn $617.50 interest
A = $7,117.50
Equation:
A = P(1 + rt)
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 9.5%/100 = 0.095 per year.
Solving our equation:
A = 6500(1 + (0.095 × 1)) = 7117.5
A = $7,117.50
The total amount accrued, principal plus interest, from simple interest on a principal of $6,500.00 at a rate of 9.5% per year for 1 years is $7,117.50.
In the figure, triangle LMN is similar to triangle PQR. Whats the length of PQ?
find the exact values of sin 2u, cos 2u, and tan 2u using double-angle formulas.
13.) sin u=3/5, 0 < u < pi/2
15.) tan u= 1/2, pi < u < 3pi/2
The exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
sin u=3/5, 0 < u < pi/2
tan u= 1/2, pi < u < 3pi/2
We need to find sin 2u, cos 2u, and tan 2u
sin2u=2sinucosu
tanu=sinu/cosu
1/2=3/5/cosu
cosu=3/5×2
cosu=6/5
So sin2u=2(3/5)(6/5)
sin2u=36/25
cos2u=1-2sin²u
=1-2(36/25)²
=1-2(1296/625)
=1-4.14
=-3.142
cos2u=-3.142
tan2u=sin2u/cos2u
Substitute the values of sin2u and cos2u
sin2u=36/25/(-3.142)
=1.44/-3.142
=-0.458
Hence, the exact values are sin2u=36/25, cos2u=-3.142 and tan2u=sin2u/cos2u
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evelyn is trying to pick out an outfit for the first day of school. she can choose from 2 pairs of pants, 2 t-shirts, and 8 pair of shoes. how many different outfits can evelyn make?
There are 32 outfits that Evelyn can make.
This is basic combination.
Evelyn has 2 shirts each shirt can be worn with each of the 2 pair of pants.
So, there are 4 ways to wear them.
she also has 8 pairs of shoes and each pair can be worn with each of the 4 outfits.
total number of outfits that she can make = 8*4
=32 outfits
Evelyn can make 32 different outfits.
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527.8317 Find the digits in the tens place, in the hundredths place, and in the thousandths place for the following number.
If a rectangle
has a width of 3w² and a
length of 2w5, write an expression to
represent the area of the rectangle.
The expression to represent the area of the rectangle is A = 6w⁷
Area of the rectangle:The rectangle is a four-sided polygon with an internal angle of 90° at the corner of every side. The opposite sides of the rectangle are equal.
The formula for the area of the rectangle is given below
Area = Length × width
Here we have
Width of the rectangle = 3w² and
Length of the rectangle = 2w⁵
As we know the area of the rectangle = Length × width
Area of the rectangle, A = 3w² × 2w⁵
=> A = 6w²×w⁵
=> A = 6w²⁺⁵
=> A = 6w⁷
Therefore,
The expression to represent the area of the rectangle is A = 6 w⁷
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A _____________ t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.
A Paired t-test evaluates data from dependent samples in which the two treatments are applied to the same individual.
T-test is a statistical statistics mainly use when population variance is unknown and sample size is small.
In Paired t-test , we compare means of two dependent samples . It gives hypothesis examination on difference between of mean.
It uses same items or people in both sample that's why they are also known as dependent t-test
Paired t-test also increases the statistical power of our analysis.
Formula of paired t-test :
[tex]t = \frac{m}{s/\sqrt{n} }[/tex] with (n-1) degree
where , m is mean difference
s is standard deviation
n is sample size
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Xylem and Phloem in plants transport water and nutrients throughout the plant similar to ______ humans.
O hormones
O blood vessels
O bones
O neurons
Answer:
blood vessels
Step-by-step explanation:
Blood vessels carry nutrients throughout your body
Answer:
Step-by-step explanation:
the answer is blood vessels.
Xylem and phloem constitute the vascular bundle. Xylem distribute and store water. Phloem is responsible for transporting sugars, proteins, and other organic material. Similarly blood vessels in humans perform the function of delivering blood that contains gases, nutrients, waste, cells and hormones throughout the body.
Laura made $342 for 18 hours of work.
At the same rate, how much would she make for 8 hours of work?
McKenzie found a correlation coefficient on a set data to be -0.20 which term describes the correlation ?
weak positive
strong negative
strong positive
weak negative
Weak positive term describes the correlation .
What does a weak positive indicate?
Negative correlation does not necessarily indicate a weak correlation between two variables. Although both variables have a tendency to rise in response to one another, a weak positive correlation suggests that the relationship between the two is not very strong.A weak positive graph is what?
Dots are used to indicate values for various numerical variables in a scatter plot, sometimes referred to as a scatter graph or scatter chart. One can see that there is a slight increase in the value of Y as the value of X increases, demonstrating a weak positive correlation.Learn more about weak positive
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y=-.06(5.5-1)(5.5-10)
Answer:
I don't know if its right.
Ans:1.215
Please someone help me with the answers I need help
Answer:
x+6, y+2
Step-by-step explanation:
x goes left and right, y goes up and down. the little ' means that is the line after translation, so w and y are the originals, and w' and y' are after the translation. Add 6 to x(left and right) (negative sign means left and positive sign or no sign means right), so go 6 to the right, and add 2 to y, so go up two (negative sign means to go down, and positive or no sign means to go up)
hey not a question but how do you ask questions with a picture on here
Answer:
the one that looks like a paper clip
Step-by-step explanation:
the points (7, 18) and (3, 14) fall on a particular line. What is its equation in slope-intercept form?
[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{14}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{14}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{7}}} \implies \cfrac{ -4 }{ -4 } \implies 1[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{ 1}(x-\stackrel{x_1}{7}) \\\\\\ y-18=x-7\implies {\Large \begin{array}{llll} y=x+11 \end{array}}[/tex]
helpp this us due by 12 its 11:49 rnn
The values of the segments formed by the median lines in the triangles are;
1. KG = 22
2. [tex]\overline{JE}[/tex] = 19.5
3. FL = 11
9) CI = 4
10) XK = 4
14) x = 3
What is a median of a triangle?A median line of a triangle is a line drawn from a vertex of the triangle to the the middle of the of the opposite side, thereby bisecting the opposite side into two segments of the same length.
The median lines are; [tex]\overline{JE}[/tex], [tex]\overline{KF}[/tex], and [tex]\overline{LD}[/tex]
1. The length of [tex]\overline{GF}[/tex] = 11
The properties of a median line indicates;
[tex]\overline{GF}[/tex] = (1/3)·[tex]\overline{KF}[/tex]
Therefore;
11 = (1/3)·[tex]\overline{KF}[/tex]
[tex]\overline{KF}[/tex] = 3 × 11 = 33
[tex]\overline{KG}[/tex] = (2/3)×[tex]\overline{KF}[/tex]
Therefore;
[tex]\overline{KG}[/tex] = (2/3) × 33 = 22
[tex]\overline{KG}[/tex] = 22
2. [tex]\overline{JG}[/tex] = 13
[tex]\overline{JG}[/tex] = (2/3) × The median line [tex]\overline{JE}[/tex]
Therefore;
[tex]\overline{JG}[/tex] = (2/3) × [tex]\overline{JE}[/tex]
[tex]\overline{JE}[/tex] = (3/2) × [tex]\overline{JG}[/tex]
[tex]\overline{JE}[/tex] = (3/2) × 13 = 19.5
3. JL = 22
[tex]\overline{KF}[/tex] is a median line, therefore, the point F is the midpoint JL
JF = FL
JL = JF + FL by segment addition postulate
JL = FL + FL = 2·FL (substitution property of equality)
JL = 22 = 2·FL
FL = 22 ÷ 2 = 11
9) CS = 6
Where CS is a median line of the triangle ΔABC, then;
CI = (2/3) × CS
CI = (2/3) × 6 = 4
10) UX = 8
Where UX is a median of the triangle ΔTUX, we get;
XK = (1/3) × UK
UX = (2/3) × UK
UK = (3/2) × UX = (3/2) × 8 = 12
XK = (1/3) × 12 = 4XK = 4
14) KL = 7·x + 1
LE = 2·x + 5
The properties of median line indicates that, KL = (2/3)·KE
LE = (1/3)·KE
Therefore;
KL = 2 × LE
7·x + 1 = 2 × (2·x + 5) = 4·x + 10
7·x + 1 = 4·x + 10
7·x - 4·x = 10 - 1 = 9
3·x = 9
x = 9 ÷ 3 = 3
x = 3
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What is a confidence interval? Choose the best description.
A range of probabilities, constructed with a sample, that describes where a population parameter will occur.
A range of values, created using a sample, within a population parameter that has a certain probability of occurring.
A range of values used to estimate where the sample statistic is likely to occur
Answer: A range of values, created using sample, within which population parameter has a certain probability of occurring.
Reason: E.g. P(a<x>b) = 0.95
confidence interval is A range of values, is created using a sample, within a population parameter that has a certain probability of occurring.
A sampling method's degree of certainty or uncertainty is measured by confidence intervals. In statistics, the probability that a population parameter will fall between a set of values for a certain percentage of the time is referred to as a confidence interval. Confidence intervals that contain either 95% or 99% of expected observations are frequently utilized by analysts. To comprehend the statistical significance of their estimates, inferences, or predictions, statisticians and other analysts employ confidence intervals.
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Reasoning Joanne cannot decide which of two washing machines to buy. The selling price of each is $720. The first is
marked down by 50%. The second is marked down by 30% with an additional 20% off. Find the sale price of each
washing machine. Use pencil and paper. Explain why Joanne should buy the first washing machine rather than the
second if the machines are the same except for the selling price.
The sale price of the second washing machine is $
(Round to the nearest dollar as needed.)
CT
Answer:
Step-by-step explanation:
First Selling price is $360, after mark down.
The second's selling price is $403, after both mark downs
Joanne should buy the first, because of the selling price after mark downs.
what is the equation of the line perpendicular to y=2x+5
Answer:
y = 1/2x + 4Step-by-step explanation:
If the line is perpendicular to y = -2x + 5 then the new line has a slope of 1/2.
So solve for b: using y = mx + b
2 = 1/2(-4) + b
2 = -2 + b
4 = b
Put it all together
y = 1/2x + 4
What is the quotient of (-168) + (-14) + (-3)? Pls help me
A: -36
B: -4
C: 4
D: 36
Answer: B: -4
Step-by-step explanation: -168/-14 = 12
12/-3 = -4
Over the set of real numbers, what is the domain of the composite function
G(F(x))?
F(x) = -x-3, G(v) = √y
G(F(x)) = √√-3-x
OA. x>-3
OB. xs-3
C. x2-3
O D. All real numbers
The domain of the composite function is - x - 3 ≥ 0 , x ≤ -3 .
The correct answer is (B).
Given,
In the question:
Over the set of real numbers.
F(x) = -x-3, G(v) = √y
G(F(x)) = √√-3-x
To find the domain of the composite function.
Now, According to the question:
Based on the given conditions:
The domain of F(x) = -x -3 is all real numbers.
The domain of
G(v) = √y is y ≥ 0
{The relationship of the domain of a composite function and the original functions}
So, - x - 3 ≥ 0 , x ≤ -3
Hence, The domain of the composite function is - x - 3 ≥ 0 , x ≤ -3 .
The correct answer is (B).
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A collector of hand-woven rugs has an oval rug that is 42 years old and a circular rug that is 14 years old. How many years ago was the oval rug five times as old as the circular rug was then?
i need an equation plsss help.
Answer:
7
Step-by-step explanation:
Gwen measured a kitchen and made a scale drawing. The scale she used was
11 inches : 5 feet. If a countertop in the kitchen is 22 inches long in the drawing, how long is
the actual counter?
As per the given ratio, the length of the actual counter is 120 feet.
Ratio:
Basically, the ratio refers an ordered pair of numbers a and b, written a / b where b does not equal 0. And a proportion is an equation in which two ratios are set equal to each other.
Given,
Gwen measured a kitchen and made a scale drawing. The scale she used was 11 inches : 5 feet.
Here we need to find the length of the actual counter if a countertop in the kitchen is 22 inches long in the drawing.
While looking into the given question, we have identified the following things,
Scale drawing ratio = 11 inches : 5 feet
And the length of the drawing = 22 inches.
When we convert the inches into feet,
Then we get,
=> 11 inches = 11/12 feet.
So the actual length can be calculated as,
=>22 : 11/12 : 5
=> 22 x 12/11 x 5
=> 2 x 12 x 5
=> 120
Therefore, the length of the actual counter is 120 feet.
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Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
4. x-int: (5,0) , (12, 0)
P (7, -4)
Answer:
y = 0.4(x - 5)(x - 12)Step-by-step explanation:
Givenx- intercepts (5, 0) and (12, 0),Point P (7, - 4).SolutionThe given translates as:
p = 5, q = 12, x = 7, y = - 4Use given x - intercepts to get the equation:
y = a(x - 5)(x - 12)Use the coordinates of P to find the value of a:
- 4 = a(7 - 5)(7 - 12)- 4 = a*2*(-5)- 4 = - 10aa = -4 / - 10a = 0.4The equation of this parabola is:
y = 0.4(x - 5)(x - 12)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{2}{5}(x-5)(x-12)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (5, 0) and (12, 0) then:
p = 5q = 12Substitute the values of p and q into the formula:
[tex]\implies y=a(x-5)(x-12)[/tex]
To find a, substitute the given point on the curve P (7, -4) into the equation:
[tex]\implies -4=a(7-5)(7-12)[/tex]
[tex]\implies -4=a(2)(-5)[/tex]
[tex]\implies -4=-10a[/tex]
[tex]\implies a=\dfrac{-4}{-10}[/tex]
[tex]\implies a=\dfrac{2}{5}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{2}{5}(x-5)(x-12)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{2}{5}(x^2-17x+60)[/tex]
[tex]\implies y=\dfrac{2}{5}x^2-\dfrac{34}{5}x+24[/tex]
kay scored 15 on quiz 1 which had a mean of 12 and standard deviation 2.4. she scored 14 on the quiz 2 which had a mean of 11 and standard deviation 2.0. in comparison to her classmates, did kay do better on quiz 1 or quiz 2?
In comparison to her classmates, Kay did better in quiz 2.
According to the question,
Kay scored 15 on Quiz 1 which had a mean of 12 and a standard deviation of 2.4
= Z-score = 15 - 12/ 2.4 = 1.25
She scored 14 on Quiz 2 which had a mean of 11 and a standard deviation of 2
= Z-score = 14 - 11/ 2 = 1.5
As we can see the Z-score of Quiz 2 is more than the Z-score of Quiz 1 hence Kay did better in Quiz 2.
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GEOMETRY PROOFS!!!!!
From given information,
6] the reason for line 2 of the proof: Given
7] the statement for line 4 of the proof: BL ≅ LK
8] the reason for line 4 of the proof: Definition of midpoint
9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL
10] the reason for line 5 of the proof: SAS postulate of triangle congruence
In this question, we have been given two triangles BWL and KTL.
We need to complete the proof.
A point L is the midpoint of line segment BK
Also, LW ≅ LT,
∠WLB ≅ ∠TLK
Consider,
Statement Reason
1) LW ≅ LT Given
2) ∠WLB ≅ ∠TLK Given
3) L is the midpoint of BK Given
4) BL ≅ LK Definition of midpoint
5) Δ BWL ≅ ΔKTL SAS postulate of triangle congruence
Therefore, from given information,
6] the reason for line 2 of the proof: Given
7] the statement for line 4 of the proof: BL ≅ LK
8] the reason for line 4 of the proof: Definition of midpoint
9] the statement of line 5 of the proof: Δ BWL ≅ ΔKTL
10] the reason for line 5 of the proof: SAS postulate of triangle congruence
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Water i draining from a conical tank at the rate of 2 m3
/min. The tank i 16 meter high
and the top radiu i 4 meter. How fat i the water level falling when the water’ level
i 12 meter high?
By using the concept of rate of change, it is obtained that
Water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
What is rate of change?
Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.
Here the concept of rate of change has been used
Let the radius of cone at any point be r m and height be h m
Volume of cone = [tex]\frac{1}{3}\pi\times r^2\times h[/tex]
Now,
By the concept of similarity,
[tex]\frac{r}{h} = \frac{4}{16}\\\\\frac{r}{h} = \frac{1}{4}\\\\r = \frac{1}{4}h[/tex]
Volume of cone (V) =
[tex]\frac{1}{3}\times \pi \times (\frac{1}{4} h)^2\timesh\\\\\frac{1}{48}\times \pi \times h^3\\[/tex]
[tex]\frac{dV}{dt} = \frac{1}{48} \times \pi \times 3h^2\times \frac{dh}{dt}\\\\\frac{dV}{dt} = \frac{1}{16} \times \pi \times h^2\times \frac{dh}{dt}\\\\[/tex]
Now,
[tex]\frac{dV}{dt} = -2,\ h = 12[/tex]
So,
[tex]-2 = \frac{1}{16}\times \pi \times (12)^2 \times \frac{dh}{dt}\\\\\frac{dh}{dt} = -\frac{2 \times 16}{\pi \times 12 \times 12}\\\\\frac{dh}{dt} =- \frac{2}{9\pi}[/tex]
So water level is falling at the rate of [tex]\frac{2}{9\pi}[/tex] m per minute
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