15100
Step-by-step explanation :
Sum of first 50 terms for the AP:
[tex]\dashrightarrow { \boxed{\sf S = \dfrac{n}{2} (2a + (n - 1)d )}}[/tex]
where ,
Total no. of terms (n)= 50 Comman difference (d) = 20 - 8 = 12 First term (a) = 8On substituting the values , we get :
[tex]\dashrightarrow \sf S = \dfrac{50}{2}(2 \times 8 + (50 - 1) \times 12) \ \\ \\ \dashrightarrow \sf S = 25(16 + 49 \times 12 ) \\ \\ \dashrightarrow \sf S = 25(16 + 588 )\\ \\ \dashrightarrow \sf S = 25(604 )\\ \\ \dashrightarrow \sf S = 15100 \\ [/tex]
[tex] \therefore[/tex] Sum of the first 50 terms is 15100
Find the nth term #2
The formula to calculate the nth term of the sequence is an = -3n+18.
What is an arithmetic progression?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
Given that the arithmetic series is 15,12,9,6.....
The nth term of the arithmetic sequence will be calculated as:-
an = a₁ + (n-1)d
The first term is 15 and the common difference for the series is 12-15 = -3.
The nth term will be calculated as:-
an = a₁ + (n-1)d
an = 15 + (n-1)-3
an = 15 -3n +3
an = -3n + 18
Therefore, an = -3n+18 is the formula to find the nth term in the sequence.
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composite functions homework
The value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.
What is composite function?In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.
Given that, h(x) = 4x + 6 and g(x) = -5x.
The value of h(g(x)) is calculated by substituting x = -5x in the equation of h(x).
h(g(x)) = 4(-5x) + 6
h(g(x)) = -20x + 6
Hence, the value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.
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What is 4x5+6n-3? It’s for my math homework due tomorrow
Answer:
=17 + 6n.
Step-by-step explanation:
[tex]4 \times 5 + 6n - 3 \\ = 20 + 6n - 3 \\ = 20 - 3 + 6n \\ = 17 + 6n[/tex]
7. The functions f(x)=2* and g(x)=8(2)* are both shown graphed.
The graph of g is certainly a vertical stretch of the function f by a
factor of 8. But, it is also a shift off by three units left. Can you
explain why this is using an exponent law?
The function g(x) = 8(2)^x is also a shift left by 3 units of f(x) = 2^x, as 8 = 2³, hence 8(2)^x = 2^(x + 3).
What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The functions for this problem are given as follows:
f(x) = 2^x.g(x) = 8(2)^x.8 is the third power of 2, hence:
8 = 2³.
When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:
8(2)^x = 2³ x 2^x = 2^(3 + x) = 2^(x + 3).
As x -> x + 3, a translation left 3 units happened.
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WILL GIVE 200 POINTS !!!!> find the x intercept and the y intercept. write each intercept as an ordered pair. y=5x-10
Answer:x intercept (2,0)
Yintercept (0,-10)
Step-by-step explanation:
y=mx+b b= y intercept
To find x you just solve
Y=5x-10
10=5x
2=x
What is the standard deviation of the discrete random variable if the variance is 1.56?
Reason:
The standard deviation is the square root of the variance.
[tex]\text{Standard deviation} = \sqrt{\text{variance}}\\\\\text{Standard deviation} = \sqrt{1.56}\\\\\text{Standard deviation} \approx 1.24899959967968\\\\\text{Standard deviation} \approx 1.25\\\\[/tex]
Round the answer however you need to, or however your teacher instructs. I rounded to two decimal places since 1.56 is to two decimal places.
The standard deviation of the discrete random variable if the variance is 1.56 is 1.25
Given that, a discrete random variable has a variance of 1.56, we need to find its standard deviation
We know that,
The standard deviation is the square root of the variance.
Standard deviation = √ variance
Standard deviation = √1.56
Standard deviation = 1.24899959967968
Standard deviation = 1.25
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what is 4y - 2x= -8 in slope-intercept form
The height of a cylinder is 20 cm. The
circumference of the base of the cylinder is 10 cm.
Which measurement is closest to the volume of the
cylinder in cubic cm?
A measurement which is closest to the volume of the cylinder in cubic cm is 158.87 cubic cm.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
Volume of a cylinder, V = πr²h
Where:
V represents the volume of a cylinder.h represents the height of a cylinder.r represents the radius of a cylinder.Next, we would determine the radius of the base of the cylinder:
Circumference of a circle = 2πr
10 = 2πr
Radius, r = 1.59 cm.
Substituting the given parameters into the volume of a cylinder formula, we have the following;
Volume of a cylinder, V = 3.142 × (1.59)² × 20
Volume of a cylinder, V = 158.87 cubic cm.
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Write a equation with the slope of 3 and goes through the point (2,5)
The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
What is the slope-point form of the line?
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is a point on the line.
Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:
y - 5 = 3(x - 2)
Expanding the right-hand side:
y - 5 = 3x - 6
Adding 5 to both sides:
y = 3x - 1
Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.
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What are the exact value of a and b?
Answer:
a = 5, b = 5√3
Step-by-step explanation:
Use sin law
sin A/a = sin C/c
sin 30/a = sin 90/10
sin 30/(sin90/10) = a
a = 5
sin B/b = sin C/c
sin 60/b = sin 90/10
sin 60/(sin90/10) = b
b = 5√3
Thomas peters purchased a new suv for $32,984. He received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. What is the final price?.
The final price of Thomas Peters' new SUV is $30,309 , can be calculated by subtracting the rebates from the initial cost.
The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:
Final Price = $32,984 - $2,175 - $500
Final Price = $30,309
Therefore, the final price of Thomas Peters' new SUV is $30,309.
It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.
By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.
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Whats the correct answer answer asap for brainlist
Answer:
this is not belongs to mathematics
Step-by-step explanation:
The 2 triangles below are similar. Find the missing side. Use your notes to help you. In your answer, type out your proportion and the solution.
PLEASE HURRY !!
The length of side DF is 5 units.
Similar Triangles :If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.
Property 1:
Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.
Property 2:
The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.
Now by property 1,
The pairs of corresponding sides of similar traingles are proportional .
Therefore, in the given triangles,
[tex]\frac{BA}{ED} =\frac{AC}{DF}[/tex]
[tex]\frac{6}{3} =\frac{10}{x} \\\\x=5[/tex]
Hence, the value of x = 5 units.
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11) Scientists studied the growth rates of two types of the flu virus. The growth rate of the first virus is modeled by the equation y = P * 3 ^ x where P is the number of people initially infected with the virus in a given population. The growth rate of the second virus could be modeled by v = P * 9 ^ x The growth rate of the second virus could be expressed as P * 3 ^ k What is the value of k? Show the work that gives your solution method. y =
The value of k is given as follows:
k = 2x.
How to obtain the value of k?The exponential function that models the growth of the first virus is given as follows:
y = P(3)^x.
The exponential function that models the growth of the second virus is given as follows:
y = P(9)^x = P(3)^k.
We have that 9 is the second power of 3, hence we have that:
y = P(3²)^x = P(3)^k.
Applying the power of power rule, we have that:
y = P(3)^(2x) = P(3)^k.
Hence the value of k is given as follows:
k = 2x.
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Find the average rate of change, problem in picture
The average rate of change of the function over the interval (-1, 2) is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
Difference quotient of a function over an interval is also the same concept as the average rate of change of a function.
Average rate of change of a function f(x) over an interval (a, b) is [tex]\frac{f(b) - f(a)}{b-a}[/tex].
Given interval is (-1, 2).
From the graph, f(-1) = -4 and f(2) = 5
Average rate = [tex]\frac{f(2) - f(-1)}{2--1}[/tex] = (5 - -4) / (3) = 9/3 = 3
Hence the given function has an average rate of change over the interval (-1, 2) at 3.
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What is the area of this shape?
8m
6m
10m
5m
Answer:
68 m²
Step-by-step explanation:
we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.
6 * 8 + 4 * 5 = remember PEMDAS
48 + 20 =
68 m²
Kevin entered a pie eating contest. He ate 4 pies in 132 seconds. How many pies can he eat in 198 seconds?
Answer:
He can eat 6 pies in 198 seconds.
Step-by-step explanation:
Divide
132÷4=33
Divide
198÷33=6 pies in 198 seconds
What is the solution to the image below?
5
10
-5
10
Answer: x=10
Step-by-step explanation:
Help with this question?
Answer:
a.18%
b.68%
Step-by-step explanation:
for a you need to multiply 2 to get 18 out of 100 to get 18% and for b you need to multiply 4 to get 68 out of 100 to get 68%
PLEASEEEEE HELPPPPP!!!
The required trigonometric ratios are as follows: sin t = 1/2 and cos t = √3/2.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
According to the given figure, we have a right triangle ΔABC which has:
AB = 1/2
BC = √3/2
CA = AB² + BC²
CA = √(1/2)² + (√3/2)²
CA = √1/4 + 3/4
CA = √4/4 = 1
As we know that the trigonometric ratios are as follows:
sin (180°- t) = AB/CA
sin t = (1/2)/1
sin t = 1/2
cos (180°- t) = BC/CA
cos t = (√3/2)/1
cos t = √3/2
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What else would need to be congruent to show that AABC= APQR by SSS?
B
A
A. AC = PQ
B. AB BA
C. BC= QR
D. ZAZP
C
Q
P
R
Given:
AC PR
AB=PQ
The condition which satisfy the congruency of the given triangle is
BC≈QR.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
To show that triangle ABC≈triangle PQR by SSS,
In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.
Given, AC≅PR, AB≅PQ.
The another one condition is BC≅QR.
Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.
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Find the area of the figure below, round to the nearest whole number.
The area of the triangle with side lengths 28 and 21 and an angle of 118 degrees is 260 squared unit.
What is the area of the given triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The area of a triangle can be determine using the formula;
A = ( a × b × sin( C ) ) / 2
From the diagram;
Side a = 28side m = 21Angle R = 118Area A = ?Plug the given values into the above formula.
A = ( a × b × sin( C ) ) / 2
A = ( a × m × sin( R ) ) / 2
A = ( 28 × 21 × sin( 118° ) ) / 2
A = ( 588 × sin( 118° ) ) / 2
A = ( 588 × 0.8829 ) / 2
A = 519.17 / 2
A = 260 square unit.
Therefore, the area of the triangle is 260 square unit.
Option D) 260 is the correct answer.
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The area of the figure to the nearest whole number is 260
Calculating the area of a triangle involving angles.The area of a triangle is the region contained by the triangle's sides. The length of the sides and internal angles affect a triangle's area differently from one triangle to the other.
From the given triangle:
The required area of a triangle is:
[tex]A = a*b * \dfrac{sin \gamma}{2}[/tex]
where;
a and b are the two sides givenγ = the given angle[tex]A = 28*21 * \dfrac{sin \ 118}{2}[/tex]
A = 14 × 21 × sin 118
A = 14 × 21 × 0.8830
A = 259.602
A = 260
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If F(x) = f(g(x)), where f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, find F'(4).
F'(4) =
Answer:
36.
Step-by-step explanation:
o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).
Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:
F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36
Therefore, F'(4) = 36.
(a) The perimeter of a rectangular parking lot is 330 m.
If the length of the parking lot is 92 m, what is its width?
Answer: Width = 73 m
Step-by-step explanation:
Perimeter = Length(2) + Width(2)
330 - (92 x 2)
330 - 184 = 146
146 = Width of 2 sides
146/2 = 73 m
Which expression does (sin 3x)(cos x) − (cos 3x)(sin x) simplify to?
cos 4x
sin -x
cos 2x
sin 2x
The given expression simplifies to sin 2x.
Option (D) is correct.
What are trigonometric ratios?
Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.
The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:
sin(A - B) = sin A cos B - cos A sin B
By comparing this formula to the given expression, we can see that:
A = 3x
B = x
Substituting these values into the formula, we get:
sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)
Hence, the given expression simplifies to sin 2x.
Option (D) is correct.
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A sample of blood pressure measurements is taken for a group of adults, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement. Find the coefficient of variation for each of the two samples; then compare the variation.
Systolic
116
130
157
94
155
122
115
138
124
122
Diastolic
82
78
74
51
89
88
56
63
72
83
Answer:
To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.
1. For the systolic sample:
•Find the mean:
mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130
•Find the standard deviation:
sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2
sum = 165.4
std = sqrt(sum/9) = 7.3
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%
2. For the diastolic sample:
•Find the mean:
mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5
•Find the standard deviation:
sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2
sum = 624.75
std = sqrt(sum/9) = 12.24
•Calculate the coefficient of variation:
CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%
So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.
a grocery store got a delivery of 24 pounds of almonds into containers of 0.75 pounds of almonds in each how many containers can they fill with almonds?
Answer:32
Step-by-step explanation: 24 divided by .75=32
For every 12 loaves of bread that a bakery bakes for sale, 5 cakes are baked. If 96 loaves of bread were baked, how many cakes would have been baked?
Answer:
Step-by-step explanation:
Here's a step by step explanation of how to calculate the number of cakes baked if the bakery baked 96 loaves of bread:
First, determine the number of sets of 12 loaves of bread that were baked:
96 loaves of bread ÷ 12 loaves per set = 8 sets of 12 loaves
Next, determine the number of cakes baked for each set of 12 loaves of bread:
For every set of 12 loaves, 5 cakes are baked.
Finally, multiply the number of sets by the number of cakes baked per set to find the total number of cakes baked:
8 sets × 5 cakes per set = 40 cakes
So, if the bakery baked 96 loaves of bread, they would have baked 40 cakes.
Answer:
40
Step-by-step explanation:
12 times 8 equals 96 and 5 times 8 equals 40, there for 40 cakes will be backed
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options.
The value of f(–10) = 82
The graph of the function is a parabola.
The graph of the function opens down.
The graph contains the point (20, –8).
The graph contains the point (0, 0).
The only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
What is a quadratic function?A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.
Given is a quadratic function f(x) = x² - 5x + 12, there are some options given, we need to select the option which are correct according to the given quadratic function,
So, firstly we will plot the graph of the given function,
From the graph, we get,
The function is a parabola which opens up, the points (20, -8) and (0, 0) do not lie in the graph,
Now, finding the value of f(-10), put x = -10
(-10)² - 5(-10) + 12 = 100+52+12 = 164
Hence, in the conclusion the only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)
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A football has a radius of 8 cm. What is the surface area of the football?
Step-by-step explanation:
A=4πr²
A = 4× 22/7 ×8²
A = 4 ×22\7×64
A=804.6m²
