the dimensions of each rectangle is 72.
What is perimeter?In geometry, a shape's perimeter is referred to as its total length. The perimeter of a form is determined by adding up the lengths of all of its sides and edges. Linear measurements like centimeters, meters, inches, and feet are used to indicate its dimensions.
EXPLANATION :
The length of a rectangle is 15 cm more than its width.
L - W = 15
Compared to the first rectangle, which has a circumference of 72 cm, the second is 2 cm smaller and 5 cm wider.
2(L-2) + 2(W+5) = 72
Simplify to get 36 L + W + 3 and 36 L + W, which equals 33 by multiplying L - 2 + W + 5 by 2.
Here, combine the two equations and apply elimination.
L - W = 15 \sL + W = 33
Using the initial length, L 2L = 48 L = 24 cm, we may find W = 24 - 15 W = 9 cm, so removing W. Second rectangle width: initial width 24 - 2 = 22 cm; second rectangle length: 9 + 5 = 14 cm.
Calculate the second rectangle's perimeter using the following equation: 2(22) + 2(14) = 44 + 28 = 72
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Select the correct scientific notation form of this numeral using only 3 significant figures. 8,468 L
8,468 written in scientific notation is 8.47 x 10³.
What is the scientific notation?Scientific notation is used to compress large numbers in smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example:
• The number : 1 x 10² is equivalent to 100
• The number 1 x 10³ is equivalent to 1000
8,468 becomes 8.47 x 10³
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Find the weighted average of these values.
Value Weight
7.00 75.0%
8.00 15.0%
9.00 10.0%
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
How to determine weighted averages?
Weighted average is a kind of average in which each element has an specific weight in contrast with uniform average, where each element has the same weight. In this problem we have three values associated to three distinct weights, whose weighted average is:
x = 0.75 · 7 + 0.15 · 8 + 0.10 · 9
x = 7.35
By using the concept of weighted averages, the weighted average of the given values is equal to 7.35.
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identify the sampling technique used for the following study. a school administrator chooses ten people at random from each class.
It is the stratified random sampling technique that was used by the school administrator.
Sampling methods are defined as how we choose members for study purposes from the population.When a person is not randomly selected which maybe it be biased somehow, the data may not be representative of the population. Stratified random sample, In this sampling, the population chosen is split first into groups ., the overall sample consists of some members from every group, and those members are chosen randomly from every group, this sampling guarantees that members from each group will be represented in the sample.
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'
Solve two thirds times v plus 6 equals one third times v minus 2.
v equals negative eight thirds
v equals eight thirds
v = −24
v = 24
The value of v in the equation is as follows:
v = -24How to express an equation?Solve two thirds times v plus 6 equals one third times v minus 2.
Therefore, the equation is as follows:
2 / 3 × v + 6 = 1 / 3 × v - 2
2 / 3v + 6 = 1 / 3 v - 2
add 2 to both sides of the equation
2 / 3v + 6 = 1 / 3 v - 2
2 / 3v + 6 + 2 = 1 / 3 v - 2 + 2
2 / 3v + 8 = 1 / 3 v
subtract 2 / 3 v from both sides
2 / 3v + 8 = 1 / 3 v
2 / 3v - 2 / 3 v + 8 = 1 / 3 v - 2 / 3 v
8 = 1v - 2v / 3
cross multiply
24 = - v
v = - 24
Therefore, v = -24
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The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11. a) find y b) find CD
The value of y = 5 and CD = 4 cm in the segment.
What is a segment ?The point D is the midpoint of a segment CF. CF = 2y-2 and CD = 3y - 11.
CD = (1/2) CF
3y - 11 = (1/2) (2y -2) (multiply both sides by 2)
6y - 22 = 2y - 2
6y - 2y = -2 + 22
4y = 20
y = 5
Substitute with the value of y in the equation of CD, you get:
CD = 3y-11 = 3(5) - 11 = 15 - 11 = 4 cm
In geometric terms, a line segment is a section of a straight line that is bordered by two clearly defined end points and contains all of the points on the line that lie inside that segment. The Euclidean distance between two endpoints of a line segment provides the length of the segment.
Between two points of a line or curve. a portion of a plane or solid figure that is eliminated due to the intersection of a line, plane, or planes, particularly one that occurs between a chord and a circle's arc.
A line segment in geometry is bordered by two separate points on a line. Another way to describe a line segment is as a piece of the line that joins two points.
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according to a report on sleep deprivation by the centers for disease control and prevention, the proportion of california residents who reported insufficient rest or sleep during each of the preceding 30 days is 8.0%, while this proportion is 8.8% for oregon residents. these data are based on simple random samples of 11,545 california and 4,691 oregon residents.
[tex]Let$p_1$ - true proportion of California residents who reported insufficient rest or sleep during the preceding 30 days$p_2$ - true proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days$\hat{p}_1$ - sample proportion of California residents who reported insufficient rest or sleep during the preceding 30 days $=0.08$$\hat{q}_1=1-\hat{p}_1=1-0.08=0.92$$n_1$ - sample size of CA residents $=11,545$[/tex][tex]$\hat{p}_2$ - sample proportion of Oregon residents who reported insufficient rest or sleep during the preceding 30 days $=0.088$$\hat{q}_2=1-\hat{p}_2=1-0.088=0.912$$n_2$ - sample size of OR residents $=4,691$The $95 \%$ Confidence Interval for $\left(p_1-p_2\right)$ is given by,$$[/tex][tex]\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{p_1 q_1}{n_1}+\frac{p_2 q_2}{n_2}}$$if $p_1$ and $p_2$ are unknown we use$$\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}}$$where $Z^*=Z_{\frac{\alpha}{2}}=Z_{0.0250}$[/tex][tex]Plugging in, we get$$\begin{aligned}\left(\hat{p}_1-\hat{p}_2\right) \pm Z^* \sqrt{\frac{\hat{p}_1 \hat{q}_1}{n_1}+\frac{\hat{p}_2 \hat{q}_2}{n_2}} \\(0.08-0.088) & \pm 1.96 \sqrt{\frac{0.08(0.92)}{11545}+\frac{0.088(0.912)}{4691}} \\&-0.008 \pm 0.009498026 \\&(-0.017498026,0.001498026) \\& \approx(-0.0175,0.0015)\end{aligned}$$[/tex][tex]a) For the Hypothesis Test we have,- i) State the hypotheses.$$\begin{aligned}&H_0: p_1-p_2=0 \\&H_1: p_1-p_2 \neq 0\end{aligned}$$[/tex]
What is hypothesis?A hypothesis test examines a suggested mathematical model to see if a sample of data contains enough evidence to disprove the null hypothesis.
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A t-shirt vendor sells yellow shirts and blue shirts at a ratio of 1:4 what percent of the shirts are yellow?
Answer: 25%
Step-by-step explanation:
Please Perform The Operation.
Add:
1.) A - 5
+ 2a - 3
2.) 5t² - 6st + 8t - 3
+ 7t² + 8st - 2t + 9
3t² + 2st + 5t + 5
Subtract:
1.) 10m - 2n - 1
- 5m - 2n + 2
2.) -5x³ + 3x² +6x
- 3x³ + 9x² + 4x
:)
The resulting polynomials are listed below:
3 · a - 8 15 · t² + 4 · s · t + 11 · t + 11 5 · m - 3 - 8 · x³ + 12 · x² + 10 · xWhat are the resulting expression by adding and subtracting polynomials?Herein we find two cases of addition of polynomials and the two cases of subtraction of polynomials. Each operation must be done by taking algebra properties into account. Complete procedures are shown below:
Addition - Case 1
(a - 5) + (2 · a - 3) Given
(a + 2 · a) + [- 5 + (- 3)] Associative and commutative properties
3 · a - 8 Distributive property / Definitions of addition and subtraction
Addition - Case 2
(5 · t² - 6 · s · t + 8 · t - 3) + (7 · t² + 8 · s · t - 2 · t + 9) + (3 · t² + 2 · s · t + 5 · t + 5) Given
(5 · t² + 7 · t² + 3 · t²) + (- 6 · s · t + 8 · s · t + 2 · s · t) + (8 · t - 2 · t + 5 · t) + (- 3 + 9 + 5) Associative and commutative properties
15 · t² + 4 · s · t + 11 · t + 11 Distributive properties / Definitions of addition and subtraction / Result
Subtraction - Case 1
(10 · m - 2 · n - 1) - (5 · m - 2 · n + 2) Given
(10 · m - 5 · m) + (- 2 · n + 2 · n) + (- 1 - 2) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
5 · m - 3 Distributive property / Cancellative property / Definition of addition and subtraction / Modulative property / Result
Subtraction - Case 2
(- 5 · x³ + 3 · x² + 6 · x) - (3 · x³ + 9 · x² + 4 · x) Given
(- 5 · x³ - 3 · x³) + (3 · x² + 9 · x²) + ( 6 · x + 4 · x) Commutative and associative properties / (- a) · (- b) = a · b / (- a) · b = - a · b
- 8 · x³ + 12 · x² + 10 · x Distributive property / Definition of addition and subtraction / Result
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f(x) = x; vertical stretch by a factor of 2 followed by a translation 1 unit up
Answer:
f(x)=2x+1
Step-by-step explanation:
Use formula:
f(x)=a(x-h)+k
a=shrinking/stretching
h= horizontal translation
left (+)
right (-)
k= vertical translation
left (-)
right (+)
find the coordinates of the points that are 17 units away from the origin and have a y-coordinate equal to −
smaller x value (x, y)=(-15,-8)
larger x value (x, y)=(+15,-8)
[tex]\sqrt{x^{2} + y^{2} } = 17[/tex]
[tex]x^{2} +y^{2} = 289[/tex]
y= -8
[tex]x^{2} =289-64[/tex]
[tex]x^{2} =225[/tex]
x= ±15
The points are (15, -8) and (-15, -8)
What do you mean by coordinates?Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematics, scientists, and engineers frequently employ a variety of coordinate systems. The positions of points in 2D or 3D are defined by two or three straight-line axes known as cartesian coordinates, sometimes known as rectangular coordinates. All scales are linear, which means that they are all graduated in uniform-sized increments. The positions of points in 2D are defined by a different coordinate system called semilog coordinates. The other scale is logarithmic while the first is linear.
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Write the standard equation for each ellipse.
25x^2+9y^2+100x+18y=116
The standard equation of each ellipse is ( 2,1)
Let a=x^2
b=y^2
And 2h=xy coefficient of term
Then the second degree equation represent an ellips hyperbola as
ab-h^2>= or <0
Here ab-h^2=225>0
The equation can be written as
(x+2)^2/9+(y-1)^2/25=1
Center c of the elips is (-2,1)
A
a=5
b=3
axis x=-2
e=✓a^2-5^2/5
=2✓14/5
As
S=S`
Cs=Cs`=✓14
ellipse=(2,1+√14) (2,1,√-14)
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Select the correct answer from each drop-down menu.
Consider the equation below.
The equation was solved using the following steps.
Step 1:
Step 2:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Complete the statements below with the process used to achieve steps 1-4.
Step 3:
Step 4:
-2(5z + 8) = 14 + 6x
-2 to 5x and 8.
6x.
16.
-16.
-10 16 = 14 + 6x
-162 16 = 14
-16z
30
-
H
11
11
11
- 15
For solve the equation there are following prpperties are used
Step -1 Distributive properties,
Step - 2 Subtraction,
Step - 3 Addition, and
Step - 4 Division.
The distributive property of multiplication , simplify expressions wherein multiply a number by a sum or difference. According to this property, the product of a sum or difference of a number is equal to the sum or difference of the products.
Given equation -
-2(5x + 8) = 14 + 6x
The equation was solved using the following steps.
Step 1: -10x - 16 = 14 + 6x
Step 2: -10x - 6x - 16 = 14 = -16x -16 = 14
Step 3: -16x = 30
Step 4: x = -30 / 16
Step 5: x = -15/8.
Complete the statements with the process used to achieve steps 1-4.
Step 1 - here we are using distributive properties
-10x -16 = 14 + 6x
distribute -2 in the parenthesis to 5x and 8
Step 2 - by subtraction method
-16x - 16 = 14
subtraction of -6x
Step 3 - Aply addition
-16x = 30
Addition of 16
Step 4 - Division
x = -30/16
division of -16
x = -15 / 8
Hence , Step- 1, 2, 3, and 4 are distributive properties, subtraction, addition, and division respectively.
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What is an equation of the line that passes through the point (4,−3) and is parallel to the line x-2y=2?
Answer:
y = 1/2x - 5
or x - 2y = 10
Step-by-step explanation:
x - 2y = 2
2y = x - 2
y = 1/2x - 1
If two lines are parallel, their slopes are equal
so m = 1/2, y = -3, x = 4
y = mx + b
-3 = 1/2(4) + b
-3 = 2 + b
b = -5
so y = 1/2x - 5
or 2y = x - 10
x - 2y = 10
Select the correct answer.
A diagram of angles 1, 2, and 3 Is shown.
Given: Angles 1 and 2 are complementary
m/1=36°
21 and 22 are
complementary
given
m21-36
given
36⁰+ m2 = 90°
definition of
complementary
angles
22 and 23 are
a linear pair
m22+ m23 = 180°
given
linear pairs theorem
What is most likely being shown by the proof?
OA m/1 + m/3 = 90°
OB. m/3 144°
OC m/1 + m/3= 180°
OD. m/3= 126°
m22=54"
subtraction
property of
equality
54+ m23=180"
substitution
property of
equality
Analyzing the given data, it cab be concluded that Option D, that is, mL3 = 126° is most likely being shown by the proof.
It can be observed from the given diagram, angle 1 and angle 2 are complementary. By the definition of complementary angles, we get the sum of angle 1 and angle 2 equal to 90°.
=> mL1 + mL2 = 90°
The value of angle 1 is given as 36.
=> mL1 = 36⁰
Using the first observed condition and the value of angle 1, we can obtain the value of angle 2.
=> 36⁰ + mL2 = 90°
=> mL2 = 90 - 36 = 54°
Therefore, the value of angle 2 is obtained as 54°.
From the diagram given in the question, it can also be inferred that angle 2 and angle 3 form a linear pair. Using the linear pair theorem, we get the sum of angle 2 and angle 3 as 180°.
=> mL2 + mL3 = 180°
Previously, we have obtained the value of angle 2 as 54°.
Hence, by substituting the value of angle 2 in the above equation, we get,
54° + mL3 = 180°
=> mL3 = 180 - 54 = 126°
Therefore, By researching all the data and the results, we can conclude that all other options are discarded and the correct option is option D.
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what is the answer i don’t understand how to do this i’m stuck please help asap i missed a week of school can you help me please? it’s very important please help
Answer:
Please see the picture below.
Step-by-step explanation:
How is the graph of g(x) = -(2x)³ related to
the graph of f(x) = x³ ?
The graph of g(x) is a vertical compression of
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal compression of
1
the graph of f(x) by a factor of 2 and a reflection
across the x-axis.
The graph of g(x) is a horizontal stretch of the
graph of f(x) by a factor of 2 and a reflection
across the y-axis.
pls help no wrong answers will report
33-2[3(3+12)-(5x2)3]
Answer:
3
Step-by-step explanation:
33 - 2[3(3 + 12) - (5 x 2)3] =
= 33 - 2[3(15) - (10)3]
= 33 - 2[45 - 30]
= 33 - 2[15]
= 33 - 30
= 3
Evaluate the expression when x = 9:
5∣∣6−x∣∣
Answer:
15
Step-by-step explanation:
Change x to the declared value: [tex]5|6-9|[/tex]
Subtract: [tex]5|6-9| = 5|-3|[/tex]
NOTE: remember that little minus big = negative of big minus little.
i.e.: 6-9 = -(9-6) = -(3) = -3
Evaluate the Absolute Value: [tex]5|-3| = 5(3)[/tex]
NOTE: remember that the absolute value of a number = the number's distance from 0 (always a positive number).
i.e.: |-2| = 2; |5| = 5
Multiply: [tex]5(3) = 15[/tex]
The craft teacher has 12 sheets of blue chart paper and 18 sheets of red chart paper. How many equal piles of chart paper can she make such that each pile has only one color?
The equal piles of chart paper that she can make such that each pile has only one color is 6.
How to illustrate the information?It should be noted that from the information, the craft teacher has 12 sheets of blue chart paper and 18 sheets of red chart paper.
In this case, the highest common factor between the numbers is 6
Therefore, the piles of chart paper that she can make such that each pile has only one color is 6.
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Par un beau dimanche ensoleilé Julien se promene
Answer:
watashiwa ana men toire ne duse ka
fipinjin desu
what is this equation 6+4÷2
Answer:
Step-by-step explanation:
6+4=10
10/2
answer =5
Please help me with this geometry question. x and pr needed ao basically like this x=(answer), PR=(answer). Thank you
Answer:
x = -1, PR = 38.
Step-by-step explanation:
As Q is the midpoint of PR
PQ = QR
6x + 25 = 16 - 3x
9x = -9
x = -1.
PR
= 6x + 25 + 16 - 3x
= 6(-1) + 25 + 16 - 3(-1)
= -6 + 25 + 16 + 3
= 38.
Thomas has a bag with 7 green marbles, 5 blue marbles, and 4 red marbles. For each part below, if the marble selected is replaced before the next marble is drawn, find the probability for the given draw. Write your answer as a simplified fraction.
A.What is the probability of getting a red marble?
B.What is the probability of getting a red or a green marble?
C.What is the probability of getting an orange marble?
Using it's concept, the probabilities are given as follows:
A. 1/4.
B. 11/16.
C. 0.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, the number of marbles is given by:
7 + 5 + 4 = 16.
Then:
For item a, 4 are red, hence the probability is 4/16 = 1/4.For item b, 4 are red and 7 are green, hence the probability is 11/16.For item c, there are no orange marbles, hence the probability is of 0.More can be learned about probabilities at https://brainly.com/question/14398287
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6 is added to the product of 7 and a number.
Answer:
7x+6
Product means multiplication
and we'll use X for "number"
and add 6
so 7x+6
The required equation model as of the given condition is 6 + 7×x.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.
Here,
Let the number be x,
6 is added to the product of 7 and a number.
= 6 + 7 × x
Thus, the required equation model as of the given condition is 6 + 7 × x.
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What is the measure of angle B if angle C is 34 degrees and angle A is unknown?
Answer:
The measure of B is 56 degrees.
Write the equation of the parabola in vertex form.
vertex (3,4), point (1,-4)
Answer:
y = - 2(x - 3)² + 4
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (3, 4 ) , then
y = a(x - 3)² + 4
to find a substitute (1, - 4 ) into the equation
- 4 = a(1 - 3)² + 4 ( subtract 4 from both sides )
- 8 = a(- 2)² = 4a ( divide both sides by 4 )
- 2 = a
y = - 2(x - 3)² + 4 ← equation in vertex form
a statistician at a metal manufacturing plant is sampling the thickness of metal plates. if an outlier occurs within a particular sample, the statistician must check the configuration of the machine. the distribution of metal thickness has mean 23.5 millimeters (mm) and standard deviation 1.4 mm. based on the two-standard deviations rule for outliers, of the following, which is the greatest thickness that would require the statistician to check the configuration of the machine? 19.3mm 19.3 millimeters 20.6mm 20.6 millimeters 22.1mm 22.1 millimeters 23.5mm 23.5 millimeters 24.9mm
As per standard deviation criteria for outliers, 26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.
What is the standard deviation?
The standard deviation, a mathematical statistic that describes how distributed evenly a dataset is in regard to its mean, is determined by taking the square root of such variance.The numbers that do not lie within two standard deviations of the mean are considered outliers by the two-standard deviation criteria for outliers.
If the mean is 23.5 mm and the standard deviation is 1.4 mm
Next, the highest thickness needs to be checked: mean Plus 2 (standard deviation)
= 23.5 + (2 *1.4)
= 26.3 mm
Therefore, 26.3 mm is the maximum thickness for which the statistician would need to examine the machine's configuration.
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Ordering 5-Digit Numbers Fill in the space below with the numbers in ascending (smallest to largest) order. 84 945 91 504 75 136, 2 94 054 85 105 93 405 73 156
We need to know about arranging numbers in an ascending order to solve the problem. The numbers arranged in ascending order is 73156, 75136, 84945, 85105, 91504, 93405, 94054.
There are two ways to arrange numbers- ascending order and descending order. Ascending order is the method of arranging numbers from lowest to highest and descending order is the method of arranging numbers from highest to lowest. To arrange 5-digit numbers in an ascending order we will need to know how to find the lowest number first. For 5-digit number we will be checking the first two digits of the number first that will tell us the numbers in tens of thousands, after we find the smallest tens of thousand in the list we follow the same process to find the consecutive numbers. If two numbers have same first two digits then we chcek the hundreds and so on. For the given question the numbers arranged in ascending order will be
73156, 75136, 84945, 85105, 91504, 93405, 94054
Therefore we found the ascending order arrangement of the 5-digit numbers which is 73156, 75136, 84945, 85105, 91504, 93405, 94054.
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When Gavin left his house in the morning, his cell phone battery was partially
charged. The charge remaining in Gavin's battery, as a percentage, can be modeled by
the equation B = 28 - 7t, where t is the number of hours since Gavin left his
house. What is the y-intercept of the equation and what is its interpretation in the
context of the problem?
B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.
What is a linear graph?
Linear graphs are straight line graphs to represent the relationship between two quantities. This graph helps in depicting a result in single straight lines. There is no use of curves, dots, bars, etc., and a straight line is denoted by the term linear. Let's represent the given example in the form of a data table.
Given equation,
B = 28 - 7t
B represents the battery percentage of the phone.
t represents time,
According to the equation, with passing of time the percentage of the battery drops.
28 is the highest amount of battery present at 0 time hours.
With passage of time the battery decreases.
So, in t = 1 hr,
battery, B = 28 - 7*1 = 28 -7 = 21%
similarly, t = 4 hrs,
B = 28 -7*4 = 28 -28 = 0%
The battery completely drains and becomes 0%
Therefore, B is the y- intercept of the equation B = 28 - 7t, where B is the percentage of the battery.
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What is the slope of the line represented by the equation f(x) = -3x + 7?