The simplified expression for the perimeter of the rectangle is 10x-30
What is perimeter of a rectangle?The perimeter of a shape is the addition of all the sides of the shape. If l is the length and w is the width, then the perimeter of a rectangle can be expressed as ;
p = 2(l+w)
The length is 3x-8 and the breadth is 2x-7
therefore the perimeter = 2( l+w)
= 2( 3x-8+2x-7)
= 2( 5x-15)
= 10x-30
therefore, the simplified expression for the perimeter of the rectangle is 10x-30
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Based on a survey of 1250 employees at a software company, the average number of hours spent in meetings per week is 4.3 with a margin of error of 1.1.
What is the range of values for the actual mean numbers of hours spent in meetings in a week? Enter your answer by filling in the blanks to correctly complete the statement.
The actual mean number of hours spent in meetings in a week is between______and______hours
Answer:
Step-by-step explanation:
The margin of error represents the range of values within which the true population mean is likely to fall with a certain level of confidence. To calculate the range of values for the actual mean number of hours spent in meetings in a week, we can use the formula:
(actual mean) = (sample mean) ± (margin of error)
Substituting the given values, we get:
(actual mean) = 4.3 ± 1.1
To find the range of values, we need to compute the upper and lower bounds of this interval:
Lower bound = 4.3 - 1.1 = 3.2 hours
Upper bound = 4.3 + 1.1 = 5.4 hours
Therefore, the actual mean number of hours spent in meetings in a week is between 3.2 and 5.4 hours.
All but 36 of the 120 state capitals have an interstate highway serving them. What percent of the capitals do not have interstates?
Therefore, 70% of state capitals do not have interstate highways serving them.
What is percent?Percent is a way of expressing a number as a fraction of 100. The term "percent" means "per hundred". Percentages are usually denoted by the symbol %, which is placed after the numerical value. Percentages are used in many fields, including finance, science, and everyday life, to represent proportions, rates, and changes in quantities.
Here,
If all but 36 of the 120 state capitals have an interstate highway serving them, then the number of capitals that do not have interstates is 120 - 36 = 84.
To find the percentage of capitals that do not have interstates, we need to divide the number of capitals without interstates by the total number of capitals and then multiply by 100:
84 / 120 x 100% = 70%
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At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get
�
x small greeting cards and
�
y large greeting cards?
Answer: 18.75
Step-by-step explanation:
small greeting cards = 1.80
large greeting cards = 3.85
1.80 x 4 = 7.20
3.85 x 3 = 11.55
7.20 + 11.55 = 18.75
One respondent said they watched 10 movies. This seems to be an
symmetrical
This graph is
skewed
to the
left
because the data is stacked on the left with a "tail" going to the right.
Most people watched
[ Select ]
movies
The graph seems to be a left symmetrical distribution and most people watched action movies
Calculating the skewness of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
From the graph, we have the following readings and observations
The movie with the highest frequency is Action moviesThe data is stacked on the right with a "tail" going to the left.Using the above as a guide, we have the following conclusions
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A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a diamond
Answer: The odds against selecting a diamond are 3:1 (or 3/4)
Step-by-step explanation: Which means that there are 3 ways to not select a diamond and only 1 way to select a diamond. The odds in favor of selecting a diamond are 1:3 (or 1/4), which means that there is only 1 way to select a diamond and 3 ways to not select a diamond.
Select the correct answer.
Consider functions f and g.
f(z) = log (x - 1)
g(x)
²-4
Which statement gives the best approximation of the solutions of the equation f(x) = g(z)?
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642
-3.464 and z≈ 3.642.
OB.
The solutions are where the graphs of the functions cross the x-axis at z
O C.
The solutions are where the graphs of the functions intersect at
-3.464 and z≈ 3.464
O D.
The solutions are where the graphs of the functions cross the x-axis at z ≈ -4 and ≈ 0.422
The statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
option A. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
How did we get the value?To find the solutions of the equation f(x) = g(x), set f(x) = g(x) and then solve for x. Using the given functions, we have:
log(x - 1) = (⅓x² - 4)
Exponentiating both sides:
x - 1 = e^(⅓x²-4)
Solve for x:
x = e^(⅓x²-4) + 1
Therefore, the solutions to the equation f(x) = g(x) are given by the values of x for which the graphs of the functions intersect. To find these points of intersection, plot the graphs of the functions and look for the points where they intersect. In other way round, solving for x numerically:
Based on the given functions, it is clear that g(x) is an upward-facing parabola with its vertex at (0, -4) and x-intercepts at (-2√3, 0) and (2√3, 0). The function f(x) is defined only for x > 1, and its graph is a monotonically increasing curve that approaches infinity as x approaches 1 from the right.
Therefore, there is only one point of intersection between the graphs of f(x) and g(x), which occurs to the right of x = 1. This point of intersection can be found numerically using a calculator or computer software, and it is approximately x ≈ 3.642.
Thus, the statement that gives the best approximation of the solutions of the equation f(x) = g(x) is:
OA. The solutions are where the graphs of the functions intersect at ≈ 1 and ≈ 3.642.
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A model rocket is launched with an initial upward velocity of 60 m/s the rocket's height h meters after t seconds h=60t-5t^2 find values for which rockets height is 30 meters
The model rocket will have a height of 30 meters at a time of 0.523 seconds and 11.477 seconds, respectively.
How to determine the time associated with the height of a rocket on air
In this problem we have the case of a model rocket being launched, the height of the rocket in time is described by the following quadratic equation:
h(t) = 60 · t - 5 · t²
Where:
h - Height, in meters.t - Time, in seconds.We need to determine the time associated to a given height of 30 meters above the ground. If we know that h(t) = 30, then the times are, respectively:
30 = 60 · t - 5 · t²
6 = 12 · t - t²
t² - 12 · t + 6 = 0
(t - 11.477) · (t - 0.523) = 0
t = 11.477 s. or t = 0.523 s.
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3.4 MIXED FACTORING
1. Utilize all of the strategies for factoring in order to factor the following polynomials.
Reminder: Combine like-terms prior to factoring.
-7n + 5n^2 + 6 - 3n^2 - 11n + 30
Answer:
2 (n - 3) (n - 6)
Step-by-step explanation:
[tex]-7n+5n^2+6-3n^2-11n+30[/tex]
Group like terms and combine...
[tex]2n^2-18n+36[/tex]
Observe that all terms contain a factor of 2. Factor out a 2...
[tex]2(n^2-9n+18)[/tex]
The leading coefficient is 1. The shortcut applies. Find the factors of "c" (18)
18 = 1 * 1818 = 2 * 918 = 3 * 6Of these factor pairs, -3 & -6 will multiply to make 18, and add to make -9 (the "b").
Finish factoring the trinomial into two binomials:
[tex]2(n-3)(n-6)[/tex]
To verify that this is a valid factoring, distribute, and recombine terms:
[tex]2(n-3)(n-6)[/tex]
[tex]2(n^2-3n-6n+18)[/tex]
[tex]2(n^2-9n+18)[/tex]
Which of the following is not a linear transformation?
Select one:
Rotation in geometry
Projection in geometry
None of the options
Reflection in geometry
MODELING REAL LIFE About 5.2% of a population
contracted the flu last year. A test used to diagnose the
flu was 92% accurate for people who had the flu and
85% accurate for people who did not have it. Find and
interpret the ratio of true positives to false positives.
The ratio of true positives to false positives, given the accuracy of the test would be 239 : 711 .
Here. we have,
First, find the number of people who have the flu:
= 5. 2 % x 10, 000
= 520 people
Those who don't have it:
= 10, 000 - 520
= 9, 480 people
True positive :
= 92 % x 520
= 478 people
False negatives:
= 8 % x 520
= 42 people
False positives:
= 15 % x 9, 480
= 1, 422 people
The ratio of true positives to false positives is therefore:
478 : 1, 422
239 : 711
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Work out the value of fg^2 when:
f = -5 and g = -4
College Level Trigonometry Question!
The force parallel to the incline that would be required to hold the monolith on this causeway is 32, 120.52 Newtons.
How to find the force ?The formula for finding the force parallel to the incline:
= mass of the monolith x acceleration due to gravity x sin( slope angle )
Mass in kg :
= 57 tons x 1000
= 57, 000 kg
Force parallel to the incline:
= 57, 000 kg x 9. 81 m/s² * sin ( 1.4 degrees )
= 57, 000 kg x 9.81 m/s² x sin ( 0.0244 radians )
= 32, 120.52 Newtons
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HELP ASAP PLEASE 20 POINTS!!!!!
Answer:
5.6 mi
Step-by-step explanation:
1 km is around 0.6 (estimate) miles so just multiply both sides by 9 and 9km = around 5.4 miles and 5.6 is the closest so it is most likely that
PLEASE HELP
Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10
The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is (9.7, 14.7).
Here, we have,
1. Identify the given information:
- Confidence level (c) = 0.95
- Sample mean (x) = 12.2
- Sample standard deviation (s) = 3.0
- Sample size (n) = 8
2. Determine the degrees of freedom (df) for the t-distribution:
- df = n - 1 = 8 - 1 = 7
3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:
- You can use a t-table or an online calculator for this.
- The t-value for a 0.95 confidence level and 7 df is approximately 2.365.
4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):
- ME = t-value * (s / sqrt(n))
- ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5
5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):
- Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7
- Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7
So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).
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can someone help me do these qustions ( sorry if its hard to see) -(geometric sequence)
1. The geometric sequence is B. -1, 2, -4, 8.
2. The sixth term is 8192.
3. The next three terms are 1, 1/2 and 1/4.
4. The 10th term is 4374.
5. The eight term is 1/16.
6. The next three terms in the geometric sequence are -1/36 1/216, and - 1/1296
7. The 8th term or the sequence will be 4.
8. The 6th term of the geometric sequence is 2048.
How to calculate the valueThe 6th term of the sequence is:
a₆ = -2 * 4⁵ = -2 * 1024 = -2048
The common ratio of the sequence is:
r = 8/16 = 4/8 = 2/4 = 1/2
16 * (1/2) = 8
8 * (1/2) = 4
4 * (1/2) = 2
Therefore, the next three terms in the geometric sequence are 8, 4, and 2.
The common ratio of the sequence is:
r = 6/(-36) = -1/6
-1/6 * (1/6) = 1/36
1/36 * (1/6) = 1/216
-1/216 × 1/6 = -1 /1296
Therefore, the next three terms in the geometric sequence are -1/36, 1/216 and 1/1296.
The 8th term or the sequence will be:
= 512 × 0.5 × 0.5 × 0.5 × 0.5⁴
= 4
The 6th term of the geometric sequence is:
= 2 × 4 × 4 × 4 × 4 × 4
= 2048
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Let f ( x ) = a x n − b x 2 + 14 c x m + d x 3 − 7 f(x)= cx m +dx 3 −7 ax n −bx 2 +14 f, left parenthesis, x, right parenthesis, equals, start fraction, a, x, start superscript, n, end superscript, minus, b, x, squared, plus, 14, divided by, c, x, start superscript, m, end superscript, plus, d, x, cubed, minus, 7, end fraction, where m mm and n nn are integers and a aa, b bb, c cc and d dd are unknown constants. Which of the following is a possible graph of y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis? Choose 1 answer:
The graph in option C is the one that best satisfies the function y = f ( x ) y=f(x)y, equals, f, left parenthesis, x, right parenthesis
How to solveThe ultimate exponent of the equation, [tex]x^n or x^m[/tex], is the key factor that determines the end behavior amid a graph.
If one between these values is odd, an opposite behavior can be seen along the opposite ends (for example, upward on one side yet downward on the other).
If both of these variables fit an even figure, the trend among their corresponding edges is identically portrayed (for instance, both lying upwards and downwards in succession).
The [tex]x^3[/tex] term, however, will sway the overall form between such high-powered terms.
Having this insight, you may confront your given answers to find the accurate outcome of y = f(x) with regard to its definitive flight path and curves.
Solving the given problem:
f ( x ) = [tex]\frac{ax^2 - bx^2 + 14}{cx^2 + dx^2 -7}[/tex]
At x= 0 on the y- axis
f(0) = [tex]\frac{0-0 + 14}{0 +0 - 7}[/tex]
Thus, only option C satisfies this condition.
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Plot and connect the points in the order listed below. When you are done, find the area of the resulting figure.
A(-7,-2)A(−7,−2), B(-3,1)B(−3,1), C(-3,4)C(−3,4), D(5,4)D(5,4), E(5,-6)E(5,−6), F(-3,-6)F(−3,−6), G(-3, -2)G(−3,−2)
The total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) has been found as 51 square units.
What is a Graph?A graph is described as a mathematical representation of a network and it describes the relationship between lines and points.
The first step is to divide the figure is into two rectangles and a triangle.
we notice that the points B, C, E, and F will form a rectangle with base BC and height of 7 units.
We also notice that the points A, D, and G form a rectangle with base AG and height 5 units.
we notice that points C, D, and E form a triangle with base CE and height 4 units.
we notice that the length of BC is 4 - 4 = 0, therefore the area of the rectangle with base BC is 0.
The area of the rectangle with base AG is (4 - (-5)) x 5 = 45 square units. The area of the triangle with base CE is (4 - 1) x 4 / 2 = 6 square units.
In conclusion, the total area of the figure with points A(-5,4), B(4,4), C(4,1), D(1,1), E(4,-3) F(4,-6), G(-5, -6) is 45 + 6 = 51 square units.
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Find the volume of the composite solid. Round your answer to the nearest hundredth.
To the nearest hundredth, the volume of composite solid, giving us 904.600 cubic metres.
specify the solid volume?How many areas of space are occupied by an object is determined by its volume. It is determined by counting how many unit cubes are required to completely fill the solid. Cubic units like cubic centimeters, cubic meters, cubic feet, etc. are used to measure the volume of solids.
For instance, the volume V of a rectangular prism with dimensions of l, w, and h can be calculated as follows:
V = l × w ×h
The composite solid has a length of 14 metres and a radius of 6 metres** and is made up of a cylinder and two hemispheres. The cylinder's volume plus twice the hemisphere's volume will add up to the entire volume.
Where r is the radius and h is the height, V = πr²h is the formula for a cylinder's volume3. Therefore, V = (6)²(14) = 504 cubic meters is the cylinder's volume.
V = (2/3)r³π where r is the radius gives the volume of a hemisphere. Therefore, V = 2(2/3)(6)³π = 2(2/3)216π = 904 cubic meters is the volume of two hemispheres.
We arrive at a total volume of 792 cubic meters by adding these volumes together.
To the nearest hundredth=904.600 cubic meters.
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A pole that is 3m tall cast a shadow that is 1.15m long at the same time a nearby building cast a shadow that is 40.75m long. How tall is the building
Answer:
The heights and shadows of the objects are legs of similar right triangles. We can use these similar triangles to set up a proportion to solve for the height of the building.
2.9 / 1.26 = x / 47.25
x = 108.75 m
200 000+40 000+8 000+10+8 in standard form
Answer:
240 8018
Step-by-step explanation:
two hundred forty eight thousand and eighteen
Mia is designing a cake for a birthday party. She plans for a total of 20 guests, each of whom may eat a piece of cake that has a volume of 8 cubic inches. Which of the following cakes would provide enough cake for each guest to have one piece of cake, with the least amount left over?
The square cake can be distributed in such a way that each person out of 15 guest may get 8 , with the least amount left over .
The Correct option is (1).
What is Volume of any shape?
The volume of an object is the amount of space occupied by the object or shape, which is in three-dimensional space. It is usually measured in terms ofof cubic units.
First find the volume of square cake,
Volume = l x b x h
= 8 x 8 x 2
=128
Now there are total 15 guests, Each of get
=
= 8.533
2.Volume of round cake (d= 6 inch, r=3 inch, h= 3 inch)
Volume=
=
=
=28.26
Now there are total 15 guests, Each of get
=
= 1.884
3.Volume of round cake (d= 8 inch, r=4inch, h= 3 inch)
Volume=
=
=
=50.24
Now there are total 15 guests, Each of get
=
= 3.349
4. Volume = l x b x h
= 6 x 9 x 2
=108
Now there are total 15 guests, Each of get
=
= 7.2
According to question each person may get 8 .
Only the square cake can be distributed in such a way that each person may get 8 , with the least amount left over .
Andy saved $32 in June, $27 in July, and $38 in August. Then Andy spent $18 on school supplies and $47 on new clothes. How much money does
Andy have left?
Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.
To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.
The total amount Andy saved is:
$32 + $27 + $38 = $97
The amount Andy spent is:
$18 + $47 = $65
To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:
$97 - $65 = $32
So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.
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Can someone please help me with this problem? I'm struggling and the assignment is already late :(
Using the following stem & leaf plot, find the five number summary and range for the data.
1 0 2
2 1 2 5 9 9
3
4 2 2 7 9
5 0 2 3 4 8 9
6 0 7
Note that the five number summary and range for the data are given as follows:
Minimum: 102First Quartile (Q1): 225Median (Q2): 329Third Quartile (Q3): 458Maximum: 607.What is the explanation for the above response?The five-number summary and range were calculated using the given stem and leaf plot. The minimum value is 102, the first quartile (Q1) is 226, the median (Q2) is 340, the third quartile (Q3) is 492, and the maximum value is 670. The range is the difference between the maximum and minimum values, which is 568.
The range is calculated by subtracting the minimum value from the maximum value:
Range: 607 - 102 = 505
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A chef has 5 containers of rice. Each container has 2 cups of rice in it. If the chef uses cup of rice for a recipe, how many cups of rice do they have left?
Answer:10-x
Step-by-step explanation:5 containers 2 cups in each. 5 x 2= 10. we don't know how many cups of rice he uses for a recipe so we call it x. Then we subtract it from the 10 cups of rice.
Bad gums may mean a bod mood. Researchers discovered that 85% of people who have suffered a bad mood had periodontal disease. Only 29% of healthy people have this disease. Suppose that in a certain community bad moods are rare, occuring with only 10% probability. If someone has periodontal disease, what is the probability that he or she will have bad mood?
Answer:
24.6%
Step-by-step explanation:
denote B: bad mood; H: healthy; D: periodontal disease
P(B|D)
=P(B,D) / P(D)
=P(B,D) / [P(D,B)+P(D,H)] ### law of total probability ###
=P(D|B)P(B) / [P(D|B)P(B) + P(D|H)P(H)]
=(0.85)*(0.1)/[(0.85)*(0.1) + (0.29)*(0.9)]
=0.245664739
A side of an equilateral triangle is 20 cm long. What is the area of the triangle
A survey asked students whether they have any siblings and pets. The survey
data are shown in the relative frequency table.
Pets
No pets
Total
Siblings
0.3
0.45
0.75
OA. 30%
OB. About 67%
O C. 75%
D. 40%
Given that a student has a sibling, what is the likelihood that he or she also
has a pet?
The likelihood that he or she has a pet given that a student does not have a sibling is 60%. Therefore, the correct option is option D.
Let A denote the event that a student does not have a sibling.
Let B denote the event that a student has a pet.
Then A∩B will denote the event that the student does not have a sibling but he has a pet.
Let P denote the probability of an event in this question.
Then, we have to find the conditional probability of event B which means the likelihood of event B occurring based on the occurrence of event A.
P(B|A)
We know that:
[tex]P(B|A) = \frac{P(A\cap B)}{P(A)}[/tex]
Also from the table, we have:
P(A)=0.25
and P(A∩B)=0.15
Hence,
[tex]P(B|A) = \frac{0.15}{0.25}[/tex]
[tex]P(B|A) = \frac{3}{5}[/tex]
[tex]P(B|A) = 0.6[/tex]
which in percentage is:
0.6 * 100 = 60 %
Therefore, the likelihood that he or she has a pet too is 60% and the correct option is option D.
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Suppose that the function is defined as follows.
Answer:
Step-by-step explanation:
True or False Deductive reasoning is when someone uses lots of data to make a conjecture.
Answer:
Step-by-step explanation:
