The definition of an angle uses the undefined term
Which equation can be solved by using this system of equations?
Answer: 3x^3-7x^2+5=7x^4+2x Is correct on edg
Step-by-step explanation:
what are the zeroes of 2x squared plus 6x minus 8
A classroom has stadium seating. There are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row and so on. There are 56 rows. What is the seating capacity of the class?
The classroom has 4,995 seats.
The classroom has 5,348 seats.
The classroom has 4,900 seats.
The classroom has 5,180 seats.
The seating capacity of the class that follows an AP is 5180.
What is an arithmetic progression?An arithmetic progression(AP) is a sequence or series of numbers such that the difference of any two successive members is a constant. The first term is a, the common difference is d, n is number of terms.
For the given situation,
There are 10 seats in the first row, 13 seats in the second row, 16 seats in the third row and so on. There are 56 rows.
This statement follows as Arithmetic Progression.
The series is 10,13,16,.....
Here [tex]a=10, d= 3[/tex]
Number of rows, [tex]n = 56[/tex]
The formula of sum of n terms of an AP is
[tex]S_{n} =\frac{n}{2} [2a+(n-1)d][/tex]
On substituting the above values,
⇒ [tex]S_{56} =\frac{56}{2} [2(10)+(56-1)3][/tex]
⇒ [tex]S_{56} =28 [20+(55)3][/tex]
⇒ [tex]S_{56} =28 [185][/tex]
⇒ [tex]S_{56} =5180[/tex]
Hence we can conclude that the seating capacity of the class that follows an AP is 5180.
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Two sides of a parallelogram measure 60 centimeters and 40 centimeters. If one angle of the parallelogram measures 132 degrees, find the length of each diagonal.
Final answer:
The lengths of the diagonals in the parallelogram can be calculated using the properties of vectors and the law of cosines with the given side lengths and angle.
Explanation:
To find the length of each diagonal in a parallelogram with sides measuring 60 centimeters and 40 centimeters and one angle of 132 degrees, we can leverage the properties of vectors and the law of cosines. It is known that one diagonal is the vector sum of the sides, while the other diagonal is the vector difference of the sides.
First, let's compute the length of the shorter diagonal, which is the vector sum of the two sides:
Shorter diagonal (Ñ) = A + B
Using the law of cosines for finding the length of a diagonal, we get:
Ѳ = 60² + 40² - 2 * 60 * 40 * cos(132°)
After computing this, we find the length of the shorter diagonal.
Next, we calculate the length of the longer diagonal, which is found by subtracting the vectors of the two sides:
Longer diagonal (D) = A - B
Again using the law of cosines:
D² = 60² + 40² - 2 * 60 * 40 * cos(48°)
After computation, we find the length of the longer diagonal.
Through these calculations using the provided formulae and the law of cosines, both diagonals' lengths can be established.
they travelled 551 km from Bagani to Zimbabwe N.R at an average speed of 75km/h and their car has an average petrol consumption of 12 litres per 100 km . calculate the following .
1. the time that it will take them to complete the journey , convert to hours & minutes .
2. the amount that they will spend on petrol if the petrol costs is R7.25 per litre ?
Make up an equation of the form y = kx +b, the graph of which passes through the following points:
P (4, 1) and Q (3, –5)
The given points are
[tex] P(4,1) , Q(3,-5) [/tex]
First we find the slope using slope formula which is
[tex] m= \frac{y_{2} - y_{1}}{x_{2}- x_{1}} [/tex]
Substituting the values of x1,y1 and x2, y2, we will get
[tex] m = \frac{-5-1}{3-4} = 6 [/tex]
Now we use slope point form, which is
[tex] y-y_{1} = m (x-x_{1}) [/tex]
Using the values of m,x1 and y1, we will get
[tex] y-1=6(x-4) \\
y-1=6x-24 \\
y = 6x-23 [/tex]
two lengths of stereo wire total 32.5 ft. one length is 2.9ft longer than the other. how long is each length of wire?
3.
Every 6 months, Reuben Lopez puts $420 into an account paying 10% compounded semiannually.
Find the account balance after 15 years.
$29,299.53
$27,904.32
$31,500.00
$29,315.00
Find all the factors of 211.
a.1 and 211
b.It has no factors
c.1, 3, 11, 20, 71, and 211
d.1, 11, 20, and 211
Final answer:
The factors of the number 211 are only 1 and 211 itself, indicating that it is a prime number. Thus, the correct answer is option a (1 and 211).
Explanation:
To find all the factors of 211, you need to determine all whole numbers that can divide 211 without leaving a remainder. Starting with the smallest factor, which is always 1, and ending with the number itself, because any number is divisible by itself, we iterate through the numbers between 1 and 211 to check if they are factors.
Through inspection or a process of trial and error, we find that there are no numbers other than 1 and 211 that can divide 211 evenly, indicating that 211 is a prime number. Therefore, the correct answer to the question 'Find all the factors of 211.' is option a. 1 and 211 are the only factors of 211
The number tiles containing the numbers 11-20 are in a bag. One tile is pulled from the bag. Determine each probability. 3a. P(prime number)= ? / 3b. p(multiple of 3)= ?
[tex] |\Omega|=10\\ [/tex]
3a
[tex] |A|=4\\\\P(A)=\dfrac{4}{10}=\dfrac{2}{5}=40\% [/tex]
3b
[tex] |A|=3\\\\P(A)=\dfrac{3}{10}=30\% [/tex]
There are only three regular polygons that can make a regular tessellation true or false
True , Therefore, there are only three polygons with regular tessellations.
What is a semi-regular tessellation?A semi-regular tessellation is a tiling of the plane by two or more regular polygons in such a way that every vertex has the same configuration of polygons in the same order. In other words, at every vertex, the same set of regular polygons meet in the same order.
Unlike regular tessellations, where only one type of regular polygon is used, semi-regular tessellations can use different regular polygons. However, the regular polygons used must have the same number of sides meeting at each vertex. For example, a semi-regular tessellation might use triangles and squares, with three triangles and one square meeting at each vertex.
Given data ,
There are actually infinitely many regular polygons that can make a regular tessellation. In fact, any regular polygon can be used to create a regular tessellation of the plane.
The number of polygons meeting at each vertex depends on the angle of the polygon, which is determined by the number of sides.
Only three regular polygons(shapes with all sides and angles equal) can form a tessellation by themselves—triangles, squares, and hexagons.
Hence , Equilateral triangles, squares and regular hexagons are the only regular polygons that will tessellate.
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Meg needs to have her car repaired. Parts will cost $905, and the labor cost for the job is $499. What will be the total cost for the job? Check your answer using the inverse operation
Two different bacteria are growing in a lab. The following functions represents the bacteria.
Bacteria A: f(x) = 1000 . 3^x, where x is number of hours.
Bacteria B: g(x) = 3000 . 2^x, where x is number of hours.
Which of the following statements are true? Select all that apply.
( )Bacteria B is growing at a fasster rate than Bacteria A.
( ) Baccteria B started with 3000 bacteria.
( ) Bacteria A doubles every three hours.
( ) Bacteria B doubles every hour.
( ) In three hours, the amount of bacteria A will be greater than the amount of Bacteria B.
Vanessa is opening a clothing store. She plans to start by selling gym shorts. It costs her $4 for each pair of shorts, $3 for ink per shorts, and $0.20 a bag. Vanessa also spends $750 on rent, $50 on electricity, and $25 on advertising each month. What is the cost function for Vanessa’s clothing store per month? A) C=4.00+825 B)C=7.20+750 C) C=7.20n+825 D)C=825n+400
Answer:7.20
Step-by-step explanation:
The correct cost function for Vanessa’s clothing store per month is,
C = 7.20n + 825
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Vanessa is opening a clothing store. She plans to start by selling gym shorts.
Here, It costs her $4 for each pair of shorts, $3 for ink per shorts, and $0.20 a bag.
And, Vanessa also spends $750 on rent, $50 on electricity, and $25 on advertising each month.
Now, Let us assume that, n represent the number of things he sell.
Hence, We can formulate;
The correct cost function for Vanessa’s clothing store per month is,
C = (4 + 3 + 0.20)n + (750 + 50 + 25)
C = 7.20n + 825
Thus, The correct cost function for Vanessa’s clothing store per month is,
C = 7.20n + 825
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Victor is enlarging a poster for a school baseball match. The graph below shows the size y of the poster after x enlargements: graph of y equals 1.8 to the power of x What does the y-intercept of the graph represent?
Answer:C
Step-by-step explanation:
Original size of the picture
If point (4,5) is in the graph of a function, which equation must be true?
Answer:
Step-by-step explanation:
C) f(4)=5
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m. The base is ___ m2. The volume is ___ m3.
The base area of the pyramid is 52900 m².
The volume of the pyramid is 2645000 m³.
Volume of a square based pyramidv = 1 / 3 B h
where
B = base area
h = height
Therefore,
Base area = 230 × 230
Base area = 52900 m²
h = 150m
B = 52900 m²
Therefore,
V = 1 / 3 × 52900 × 150
V = 7935000 / 3
V = 2645000 m³
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Experts/ace/geniuses helppp asapp
Factor the expression. 40z – 20
a) 2z - 1
b) 2(20z-10)
c) 20(2z-1)
d) 20(2Z-20)
Answer:
[tex]\bf\pink{20(2z-1)}[/tex]Step-by-step explanation:
Given Expression :-[tex]\rm\gray{40z-20}[/tex]Steps to factorise :-[tex]\\\to\:\:\to\:\:\rm\red{40z - 20}[/tex]
Factor out [tex]\bf\blue{20}[/tex] from the expression[tex]\\\to\:\:\to\:\:\rm\green{20(2z-1)} \\ [/tex]
(Refer the attachment for graph representation)
Graph Details :-[tex]\bigstar\:\:\bf\purple{y = 40z-20} \\ [/tex]
[tex]\rm{Root \: \bigg( \dfrac{1}{2}, \:0\bigg) }[/tex][tex]\rm{ Domain \: \:z \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Range \: \:y \: \in\:{\mathbb{R}}}[/tex][tex]\rm{Vertical \: intercept\:\:(0,\:-20)}[/tex]Graph the inequality y<|x+2|. Which point is not part of the solution?
A) -1,-2
B) 1,2
C) 0,0
D) -1,2
Answer:
D) (-1, 2)
Step-by-step explanation:
See the graph below. The indicated point is not in the shaded region, hence not part of the solution.
What is the following sum? 4(5 sqrt x^2y)+3(5 sqrt x^2y)
Answer:
7(5 sqrt x^2y) or C
Step-by-step explanation:
in 2000, Jonesville had a population of 15,000. in 2001, the population was 16250 and in 2002, the population was 17,500. if the population grew at the same constant rate each year, which model describes the population growth for n years after 2000?
In year 2000, the population was 15,000.
In year 2001, the population was 16,250.
In year 2002, the population was 17,500.
The population growth from year 2000 to year 2001 was (16,250-15,000) = 1,250.
The population growth from year 2001 to year 2002 was (17,500-16,250) = 1,250.
So the slope of the line would be m = 1250.
And y-intercept would be the initial population i.e. b = 15,000.
So the equation of line is y = 1250x + 15000.
Hence, n years after 2000, the population would be P = 1250n + 15000.
If it takes 2 nurses 2 minutes to measure the blood pressure of 2 patients, how long would it take 200 nurses to measure the blood pressure of 200 patients (in minutes)?
Answer:
it will take 2 minutes for 200 nurses to measure the blood pressure of 200 patients .
Step-by-step explanation:
We know that the work-time and number of labor and efficiency formula is given by:
[tex]Efficiency=\dfrac{Number\ of\ labor\times Time}{Work\ done}[/tex]formula is given by:
Here Number of labor=Number of nurses.
Work=Number of patients whose blood pressure were noted.
As the efficiency will be same this means that:
[tex]\dfrac{2\times 2}{2}=\dfrac{200\times x}{200}[/tex]
where x denotes the number of time taken by 200 nurses.
Hence,
[tex]x=2[/tex]
Hence, the answer is:
2 minutes.
Q7 Q19.) Find the area of the triangle having the given measurements.
Past experience indicates that the time re- quired for high school seniors to complete a standard- ized test is a normal random variable with a standard deviation of 6 minutes. test the hypothesis that σ = 6 against the alternative that σ < 6 if a random sample of the test times of 20 high school seniors has a standard deviation s = 4.51. use a 0.05 level of significance.
At 0.05 level of significance, there is sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6.
To test the hypothesis that the standard deviation ([tex]\sigma = 6[/tex] ) against the alternative that ( [tex]\sigma = 6[/tex] ), we can use a chi-square test.
The test statistic for a chi-square test is given by ( [tex]\chi^2 = \frac{(n-1)s2}{\sigma2}[/tex]), where:
The sample size = [tex]n[/tex]
The sample standard deviation = [tex]s[/tex]
The hypothesized standard deviation = [tex]\sigma[/tex]
The sample size, n = 20
The sample standard deviation, s = 4.51
The hypothesized standard deviation, [tex]\sigma[/tex] = 6
Substituting these values into the formula:
[tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex]
The degrees of freedom for the test is ( n - 1 = 20 - 1 = 19 ).
The test statistic for our chi-square test is ([tex][ \chi^2 = \frac{(20-1)(4.51)2}{62} \approx 14.13 ][/tex] ).
The critical value for a chi-square distribution with 19 degrees of freedom at the 0.05 level of significance is approximately 30.14.
Since our test statistic ([tex]\chi^2 = 14.13[/tex] ) is less than the critical value (30.14), we reject the null hypothesis that [tex]\sigma[/tex] = 6 at the 0.05 level of significance.
Thus, we have sufficient evidence to support the alternative hypothesis that [tex]\sigma[/tex] < 6, suggesting that the standard deviation of the time required for high school seniors to complete the standardized test is less than 6 minutes.
Help Please
Find the difference of 217.64 and 59.372
Round to the nearest whole number and find the difference
Use front- end rounding and find the difference
Find the exact (precise) difference.
1) The precise difference is 158.268.
2) The difference when rounded to the nearest whole number is 159.
3) the difference using front-end rounding is 150.
1) To find the difference, subtract the smaller number from the larger number:
[tex]217.64 - 59.372 = 158.268[/tex]
2) First, let's round each of the numbers to the nearest whole number.
217.64 rounds to 218.
59.372 rounds to 59.
Now, subtract these rounded numbers:
[tex]218 - 59 = 159[/tex]
3) Front-end rounding means rounding the numbers based on the left-most digit (or most significant digit). For simplicity, we will keep the first digit and change the others to zeros.
217.64 can be rounded to 200.
59.372 can be rounded to 50.
Now, subtract these rounded numbers:
[tex]200 - 50 = 150[/tex]
the weight of an object on mars varies directly with its weight on earth. an object that weighs 50 pounds on mars weighs 150 pounds on earth. if an object weighs 120 pounds on earth, write and solve a direct variation equation to find how much an object would weigh on mars.
To find the weight of an object on Mars, we can use a direct variation equation. By finding the constant ratio from the given values, we can then solve for the weight on Mars when the weight on Earth is known. In this case, the object would weigh 40 pounds on Mars if it weighs 120 pounds on Earth.
Explanation:To solve this problem, we will use the concept of direct variation. The weight of an object on Mars varies directly with its weight on Earth. This means that the weight on Mars can be found by multiplying the weight on Earth by a constant ratio. Let's represent the weight on Mars as WM and the weight on Earth as WE. According to the problem, an object that weighs 50 pounds on Mars weighs 150 pounds on Earth. This gives us the following direct variation equation:
WM = k * WE
where k is the constant ratio.
We can now substitute the given values: 50 pounds for WM and 150 pounds for WE.
50 = k * 150
To solve for k, divide both sides of the equation by 150:
k = 50 / 150
k = 1 / 3
Now that we have the value of the constant ratio, we can find the weight of an object on Mars when it weighs 120 pounds on Earth. Let's represent the weight on Mars as x and the weight on Earth as 120:
x = (1 / 3) * 120
x = 40
Therefore, the object would weigh 40 pounds on Mars.
What is the square root 25 multiplied by 40 divided by 2
Write the linear equation 5x-15y=-8 in slope-intercept form.