The sum of the 24 terms of the arithmetic series is 900
How to solve:
To find the sum of an arithmetic series, we can use the formular:
Sn = (n/2)(2a + (n-1)d)
Where;
Sn is the series sum, n is the number of terms, a is the first term, and d is the common difference.
The first term (a) in this scenario is 3, and the common difference (d) is 3. With n equal to 24, we want to find the sum of the first 24 terms.
When the values are entered into the formula, we get:
The sum of the first 24 terms of the arithmetic series is 900 because;
S24 = (24/2)(2(3) + (24-1)(3))
= 12(6 + 23(3))
= 12(6 + 69)
= 12(75)
= 900.
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Giselle works as a carpenter and as a blacksmith.
She earns
$
20
$20dollar sign, 20 per hour as a carpenter and
$
25
$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of
30
3030 hours, and earned a total of
$
690
$690dollar sign, 690.
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answer:
Giselle worked as a carpenter for 12 hours and as a blacksmith for 18 hours last week
Step-by-step explanation:
Let's assume that Giselle worked as a carpenter for x hours and as a blacksmith for y hours last week.
We know that she earns $20 per hour as a carpenter and $25 per hour as a blacksmith, and that she worked a total of 30 hours, so we can write two equations based on this information:
x + y = 30 (total hours worked)
20x + 25y = 690 (total earnings)
To solve for x and y, we can use substitution or elimination. Let's use substitution.
From the first equation, we can solve for x in terms of y:
x = 30 - y
Substitute this expression for x in the second equation:
20(30 - y) + 25y = 690
Simplify and solve for y:
600 - 20y + 25y = 690
5y = 90
y = 18
So Giselle worked as a blacksmith for 18 hours last week.
To find how long she worked as a carpenter, we can substitute y = 18 into the first equation and solve for x:
x + 18 = 30
x = 12
Therefore, Giselle worked as a carpenter for 12 hours last week.
The following are the populations for the top twelve largest cities in the U. S. New York City, NY: 8,336,817 Los angeles CA: 979.576 Chicago, il:2,693,976 Houston, TX: 2,320,268 Phoenix AZ: 1,680,992 Philadelphia PA: 1,584,064 San Antonio TX: 1, 547,253 San Diego CA: 1,423,851 Dallas TX: 1,343,573 San Jose CA: 1,021,795 Austin TX:978,908 Jacksonville FL: 911,507. What is the mean population?, what is the median population?, what is the mode?, what is range?, what is the standard Deviation?
Mean: Mean = (8,336,817 + 979,576 + 2,693,976 + 2,320,268 + 1,680,992 + 1,584,064 + 1,547,253 + 1,423,851 + 1,343,573 + 1,021,795 + 978,908 + 911,507) / 12=2688602
Median = 1,643,032
Mode: Determine the value(s) that appear most frequently in the population list. In this case, there is no mode as none of the population values repeat.
Range = 8,336,817 - 911,507 = 7,425,310.
Standard Deviation = √( Σ ( xi - μ )² / N )
To find the mean, median, mode, range, and standard deviation of the given population data for the top twelve largest cities in the U.S., we can perform the following calculations:
Performing these calculations will yield the mean population, median population, mode (if any), range, and standard deviation of the given population data for the top twelve largest cities in U.S .
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The weight (in kilograms) of 14 patients were measured as 59, 63, 61, 62, 58, 60, 58, 57, 57, 56, 50, 69, 58 and 50. What is the range weight (in kilograms) of these patients?
Answer:
57 kilograms. .........................................................................kg
pls pls help, will give brainliest answer!!
Answer:
Equation of the triangle: (x + 74) + 73 + (37 + x) = 180°
Solve for x: x = -2
Find the measure of angle A: A = 35°
Step-by-step explanation:
Step 1: We know that the 73° angle and the angle inside the triangle that lies opposite it are vertical angles ,so this angle is also 73° .
Step 2: Similarly, the (x + 74)° angle and the angle inside the triangle that lies opposite it are also vertical angles, so this angle is also represented by the expressions (x + 74)°
Equation of the triangle: The triangle sum theorem states that the sum of the interior angles of a triangle equals 180°. Thus, the equation of the triangle is (x + 74) + 73 + (37 + x) = 180
Solving for x:
Step 1: Rearrange and combine like terms:
(x + 74) + 73 + (37 + x) = 180
(x + x) + (74 + 73 + 37) = 180
2x + 184 = 180
Step 1: Subtract 184 from both sides:
(2x + 184 = 180) - 184
2x = -4
Step 3: Divide both sides by 2 to solve for x:
(2x = -4) / 2
x = -2
Finding the measure of angle A: Now we can plug in -2 for x in the expression representing the measure of angle A to find the actual measure:
A = 37 - 2
A = 35
Thus, the measure of angle A is 35°.
Optional Step: We can check that our equation of the triangle, the value we've found for x, and the measure of angle A is correct by simply plugging in -2 for x in the equation of the triangle and checking that we get 180 on both sides:
(-2 + 74) + 73 + (37 - 2) = 180
72 + 73 + 35 = 180
145 + 35 = 180
180 = 180
Thus, all of our answers are correct.
Anybody know this? Find the first four terms of the sequence t/n=n(6n-2) the n is below the t btw
The first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
How to find st four terms of the sequenceLet's substitute n = 1:
t/1 = 1(6(1) - 2)
t = 1(6 - 2)
t = 4
The first term of the sequence (when n = 1) is 4.
Now, let's substitute n = 2:
t/2 = 2(6(2) - 2)
t = 2(12 - 2)
t = 2(10)
t = 20
The second term of the sequence (when n = 2) is 20.
Next, let's substitute n = 3:
t/3 = 3(6(3) - 2)
t = 3(18 - 2)
t = 3(16)
t = 48
The third term of the sequence (when n = 3) is 48.
Lastly, let's substitute n = 4:
t/4 = 4(6(4) - 2)
t = 4(24 - 2)
t = 4(22)
t = 88
The fourth term of the sequence (when n = 4) is 88.
Therefore, the first four terms of the sequence t/n = n(6n - 2) are: 4, 20, 48, 88.
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find the perimeter of a rectangle if: L= 12cm, W= 5cm.
(a) 34cm
(b) 21cm
(c) 14cm
(d) 17cm
Answer:
(a) 34 cm
Step-by-step explanation:
The formula for perimeter of a rectangle is
P = 2l + 2w, where
P is the perimeter,l is the length,and w is the width.Thus, we can plug in 12 for l and 5 for w in the perimeter formula and simplify to find the perimeter of the rectangle:
P = 2(12) + 2(5)
P = 24 + 10
P = 34
Thus, the perimeter of a rectangle with a length of 12 cm and a width of 5 cm is 34 cm.
Please help me find the function that explains how to get the output from the input
Answer:
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
Step-by-step explanation:
For this, first search for the Slope of the funtion
THe slope can be found by calculating this :
(y2-y1)/(x2-x1) or in this case (output2 - output1)/ (input2 - input1)
IT continues as follows:
( -48.5 - 24) / (-413 - (-703) ) =
= (-72.5) / (290)
= -0.25
The slope is -0.25. If the function is a line then the equation is
-0.25*input + B = output
with any of the choices we can determine B.
-0.25 * (-703) + B = 24
175.75 + B = 24
175.75 +B - 175.75 = 24 - 175.75
B = - 151.75
The equation for those inputs and outputs is:
0.25 *input - 151.75 = Output
What is the area of the shaded region?
Answer:
80 mm²
Step-by-step explanation:
Even for slanted triangles, the area is base x half height! The base is 10 mm, half the height is 8 mm, so the area is 8x10=80 mm.
Question
Which equation describes the pattern shown in the table?
The equation of the quadratic function is y=x2−4x, the correct option is E
We are given that;
x=-4,-2,1
y=5,-5,0
Now,
The first three rows of the table, we get:
y=−4 when x=−5y=5 when x=−2y=−3 when x=1
Substituting into the general form, we get:
−4=25a−5b+c5=4a−2b+c−3=a+b+c
Solving this system of equations, we get:
a=1b=−4c=0
Therefore, the equation of the quadratic function is y=x2−4x.
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Question 5
TABLE 4 below shows the distribution of revenue among the different spheres of
government in South Africa from the 2017/2018 to 2021/2022 financial year. Some values
have been omitted.
TABLE 4: Distribution of Revenue among the different government spheres for
the financial years 2017/2018 to 2021/2022.
R(billion)
2019/20
546.1
471,4
Government
BHOJDIN
National
Provincial
Local
TOTAL
2017/18
453.4
410.6
**
2018/19
490,00
439,5
87.6
1 017,1
98.3
1:15.8
2020/21
557,5
500,4
103.3
1 161.2
2021/22
1 240.5
(adapted from DBE 2014 MLQP)
Use the table above to answer questions that follows
When the revenue of the local government sector was compared to the provincial sec
2017/18, it was found to be 20, 12% of the provincial sector.
Calculate
the missing value E, the total revenue for the period 2017/18.
ont sector always receives a larger share than t
The missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.
How to calculate the valueLocal government sector's revenue in 2017/18 (L): Missing value (to be calculated)
Provincial sector's revenue in 2017/18 (P): 410.6 (billion)
According to the information provided, L is 20.12% of P. Mathematically, we can write this as:
L = 20.12/100 * P
Substituting the known value of P, we get:
L = 20.12/100 * 410.6
L ≈ 82.61 (rounded to two decimal places)
Therefore, the missing value E, the total revenue for the period 2017/18, is approximately 82.61 billion.
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What is the value of x?
Answer:
x = 24.5
Step-by-step explanation:
27/(x + 7) = (27 - 6)/x
27x = (x + 7)(21)
27x = 21x + 147
6x = 147
x = 24.5
Answer:
x = 31.5
Step-by-step explanation:
given a line parallel to a side of a triangle and it intersects the other two sides then it divides those sides proportionally , that is
[tex]\frac{6}{27-6}[/tex] = [tex]\frac{7}{x}[/tex]
[tex]\frac{6}{21}[/tex] = [tex]\frac{7}{x}[/tex] ( cross- multiply )
6x = 21 × 7 = 147 ( divide both sides by 6 )
x = 24.5
Find the area of a triangle whose base (b) is 5 feet and whose height (h) is 2 ft.
(a) 5ft.²
(b) 20ft.²
(c) 100ft.²
(d) 3.5ft.²
Answer:
(a) 5 ft^2
Step-by-step explanation:
The formula for area of a triangle is given by the formula,
A = 1/2bh, where
A is the area in square units,b is the base,and h is the height.Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:
A = 1/2(5)(2)
A = (5/2)(2)
A = 10/2
A = 5
Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2
Now, let’s rewrite our point-slope equation in slope-intercept form.
y−6=−2(x+2)
y−6=
x−4
y=−2x+2
Is this the same equation we got when we wrote it in slope-intercept form earlier? YES!
Any equation written in point-slope form can be rewritten in slope-intercept form and most of the time, we will rewrite them. Slope-intercept form is the most popular and used form of linear functions/equations. In Slope-intercept form, all like terms have been combined, therefore it is in simplified form. Remember that we always want the most simplified answer possible, unless otherwise directed!
The equation in slope-intercept form is,
y = - 2x + 2
We have to given that;
The point-slope equation is,
y - 6 = - 2 (x + 2)
Now, We can rewrite the equation in slope-intercept form as;
y - 6 = - 2 (x + 2)
y - 6 = - 2x - 4
y = - 2x - 4 + 6
y = - 2x + 2
Thus, the equation in slope-intercept form is,
y = - 2x + 2
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A toy ball can be modeled as a sphere. Jeriel measures its diameter as 21.9 cm. Find
the ball's volume in cubic centimeters. Round your answer to the nearest tenth if
necessary.
Answer:
Step-by-step explanation:
A rectangle has an area of 114cm squared and a perimeter of 50cm. What are the dimensions
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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Which of the following could be used to calculate the area of the sector in the circle shown above?
The area of the sector in the circle shown above is given as follows:
32.3 in².
How to calculate the area of a circle?The area of a circle of radius r is given by the multiplication of π and the radius squared, as follows:
A = πr²
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, hence it is given as follows:
r = 10 in.
Then the area of the entire circle is given as follows:
A = π x 10²
A = 314 in².
The entire circumference of the circle is of 360º, while the angle is of 37º, hence the area of the sector is given as follows:
37/360 x 314 = 32.3 in².
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Evaluate the following statement.
( - 179 – 78 ) + 41 - ( - 165 )
The answer is:
( - 179 – 78 ) + 41 - ( - 165 )
=-51
Answer:
(-257) +41+165
-257+206
-51
6 sinθ=5 to the nearest 0.1°
The value of the equation 6 sinθ=5 for θ is 56.4 degrees
How to evaluate the equationFrom the question, we have the following parameters that can be used in our computation:
6 sinθ=5
Express the equation properly
So, we have the following representation
6 sin(θ) = 5
Divide both sides of the equation by 6
This gives
sin(θ) = 5/6
Evaluate the quotient
sin(θ) = 0.833
Take the arc sin of both sides
θ = sin⁻¹(0.833)
Evaluate
θ = 56.4
Hence, the value of the equation for θ is 56.4 degrees
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Complete question
Approximate θ in the equation, to the nearest 0.1 degrees
6 sin(θ) = 5
15(2x -10) + 4x= -3(15x + 4)
The value of x in the equation 15(2x - 10) + 4x = -3(15x + 4) is 1.7
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operators.
Given the equation:
15(2x - 10) + 4x = -3(15x + 4)
Solving the parenthesis:
30x - 150 + 4x = -45x - 12
Collect like terms:
30x + 4x + 45x = -12 + 150
79x = 138
Dividing both sides by 79:
x = 1.7
The value of x is 1.7
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You pay for a fiction book, a nonfiction book, and a bookmark with three $5 bills. The fiction book costs $5.43. The nonfiction book costs $3.89. Your change is $3.45. How much does the bookmark cost?
Answer:
2.23
Step-by-step explanation:
You have 3 $5 bills which us 15 dollars. 15 dollars - 5.43 - 3.89 - 3.45 = 2.23 dollars for the bookmark.
To see if you are correct, you can add 3.45, 2.23, 3.89, and 5.43 to get your answer.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
A
Step-by-step explanation:
i do this all the time math is my thing
Please someone help me with this. Simplify. The expression in the picture no negative exponents should be added in the answer
A simplification of the given expression is 1/m¹⁶.
What is an exponent?In Mathematics, an exponent is a mathematical operation that is commonly used in conjunction with an algebraic equation or expression, in order to raise a given quantity to the power of another.
Mathematically, an exponent can be represented or modeled by this mathematical expression;
bⁿ
Where:
the variables b and n are numbers (numerical values), letters, or an algebraic expression.n is known as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the given algebraic expression, we would have the following simplified expression:
[tex](m^{\frac{4}{5}} \cdot m^{\frac{4}{5}} )^{-10}\\\\(m^{\frac{4}{5} +\frac{4}{5} } } )^{-10}\\\\(m^{\frac{8}{5} } )^{-10}\\\\(m^{\frac{8 \times -10}{5} } )\\\\(m^{\frac{-80}{5} } )\\\\m^{-16}[/tex]
1/m¹⁶
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
4x = 100, so x = 25
The correct answer is C.
3. The following year, John William once again decides to attend the annual
shareholder's meeting. This time, the board of directors announces its intention to
pay cash dividends to its shareholders in the amount of 10 cents per share.
a. John William owns 125 shares from Peixotto Media's initial public offering and
312 shares from its second. What dividend will he receive? (2 points)
b. Peixotto Media's stock price is currently at $7.25 per share. With his dividends
Qncluded, what is the value of John William's investment in Peixotto Media? (3
points)
John William will receive a total dividend of $43.70.
The value of John William's investment in Peixotto Media, including dividends, is $3,216.95.
a. John William owns a total of 125 + 312 = 437 shares in Peixotto Media. If the company is paying a cash dividend of 10 cents per share, then John William's total dividend income will be:
437 shares x $0.10 per share = $43.70
Therefore, John William will receive a total dividend of $43.70.
b. If John William owns 437 shares in Peixotto Media and the current stock price is $7.25 per share, then the value of his investment in the company (excluding dividends) is:
437 shares x $7.25 per share = $3,173.25
If we add the dividend income of $43.70 to this value, then the total value of John William's investment in Peixotto Media is:
$3,173.25 + $43.70 = $3,216.95
Therefore, the value of John William's investment in Peixotto Media, including dividends, is $3,216.95.
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Mrs horwitz is wrapping a present in a rectangular prism box for mr roberts. the dimensions of the gift are 13 in by 8 in by 11 in. how much wrapping paper does she need. should mrs horwitz find the volume or surface area to figure out how much wrapping paper she needs. based on your answer above, find the solution. show all your work
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
We have,
To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given dimensions:
Length (l) = 13 in
Width (w) = 8 in
Height (h) = 11 in
Plugging these values into the formula, we get:
Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)
Surface Area = 208 + 286 + 176
Surface Area = 670 in²
Therefore,
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
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On Saturday, a local hamburger shop sold a combined total of 234 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Saturday?
Answer:
78
Step-by-step explanation:
Let the number of hamburgers sold = x.
Then, the number of cheeseburgers sold = 2x.
Total number of sales: x + 2x = 3x
Total number of sales: 234
3x = 234
x = 78
Answer: 78
Can someone please answer and provide an explanation for these problems?
Answer:
50) Midpoint: (5.5, 0)
51) Midpoint: (6, -8)
Step-by-step explanation:
We can find the midpoint between two points using the midpoint formula, which is m = (x1 + x2) / 2, (y1 + y2) / 2, where
m is the midpoint,(x1, y1) are one point,and (x2, y2) are another point50) We can allow (10, 10) to be our (x1, y1) point and (1, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (10, 10) and (1, -10):
(10 + 1) / 2
11 / 2
5.5
y-coordinate of midpoint of (10, 10) and (1, -10):
(10 + (-10)) / 2
(10 - 10) / 2
0 / 2
0
Thus, the midpoint of the line segment with the endpoints (10, 10) and (-1, 10) is (5.5, 0).
51) We can allow (3, -6) to be our (x1, y1) point and (9, -10) to be our (x2, y2) point:
x-coordinate of midpoint of (3, -6) and (9, -10):
(3 + 9) / 2
12 / 2
6
y-coordinate of midpoint of (3, -6) and (9, -10):
(-6 + -10) / 2
(-16) / 2
-8
Thus, the midpoint of the line segment with the endpoints (3, -6) and (9, -10) is (6, -8).
Four points are plotted on the number line. Which point best represents 33 1/3% of the distance between zero and one
The point Y best represents 33 1/3% of the distance between zero and one.
We know that if the mixed fraction a b/c can expressed as improper fraction in below way:
a b/c = (a*c + b)/c
Here the given the mixed fraction is = 33 1/3 = (33*3 + 1)/3 = 100/3
The distance between the point 0 and 1 is given by = 1 - 0 = 1
So the required percentage of the distance = 1*(33 1/3%) = 1*(100/3 %) = 100/(3*100) = 1/3.
From the number line given we can see that the distance between 0 and 1 is divided in to 12 equal parts.
So, 33 1/3% stands at = 12*(1/3) = 4 th parts that is point Y.
Hence the point Y best represents 33 1/3% of the distance between zero and one.
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The question is incomplete. The complete question will be -
- Darrell Morris has a family plan. The HMO annual premium is $12,240. The employer pays 90% of the cost.
a) How much is Darrell's annual contribution? b) How much is his semimonthly deduction?
Answer:The employer pays .90 * 12240 = $ 11016. The emplyee pays .10 *12240 = $ 1224 = annual contribution. Contribution rate = (100% - 90%) = 10%.
Step-by-step explanation:
Answer:
a) $1,224
b) $51
Step-by-step explanation:
a) To calculate Darrell's annual contribution, we need to determine the portion he pays out of the total premium.
Given that the employer pays 90% of the cost, Darrell is responsible for the remaining 10%.
Annual contribution = Total premium × 10%
= $12,240 × 0.10
= $1,224
Therefore, Darrell's annual contribution is $1,224.
b) To find Darrell's semimonthly deduction, we divide his annual contribution by the number of semimonthly periods in a year.
Number of semimonthly periods in a year = 12 (months) × 2 (semimonthly periods per month) = 24
Semimonthly deduction = Annual contribution / Number of semimonthly periods
= $1,224 / 24
= $51
Therefore, Darrell's semimonthly deduction is $51.
Hope this helps!
Adam’s prepaid card charges a one-time opening fee and a monthly fee. The table below shows his total fees after x months.
x # of months y total fees ($)
2 27
3
4
5 60
a. How much is the initial opening fee?
b. How much is the monthly maintenance fee?
c. Write an equation to model Adam’s fees over time.
Based on a system of equaitons, the initial opening fee (one-time payment) is $5.00, the monthly maintenance fee is $11.00, while an equation that models Adam's fees over time in months, x is y = 11x + 5.
What is a system of equations?A system of equations or simultaneous equations are two or more equations solved concurrently or at the same time.
An equation is a mathematical statement showing the equality or equivalence of two or more algebraic expressions.
While algebraic expressions combine variables with numbers and mathematical operands, equations use the equal symbol (=).
Total Fees after x months
x = # of months y = total fees ($)
2 27
3 38 (11 x 3 + 5)
4 49 (11 x 4 + 5)
5 60
Let w = the monthly maintenance fee
Let z = the one-time opening fee
Equations:5w + z = 60 ... Equation 1
2w + z = 27 ... Equation 2
Subtract Equation 2 from Equation 1:
3w = 33
w = 11
b) The monthly maintenance fee is $11.00.
a) The initial (one-time) opening fee is $5.00.
z = 60 - 55
= 5
c) The total fees after x months is y = 11x + 5.
Thus, the one-time opening fee and the monthly maintenance fee can be computed using a system of equations.
Learn more about system of equations at https://brainly.com/question/13729904.
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