Answer:
- 30
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence
d = 34 - 40 = 28 - 34 = 22 - 22 = - 6
This indicates the sequence is arithmetic with sum to n terms calculated as
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = - 6, thus
[tex]S_{15}[/tex] = [tex]\frac{15}{2}[/tex] [ (2 × 40) + (14 × - 6) ], that is
[tex]S_{15}[/tex] = 7.5(80 - 84) = 7.5 × - 4 = - 30
Answer:
[tex]\displaystyle -44 = s_{15}[/tex]
Step-by-step explanation:
[tex]\displaystyle -6n + 46 = a_n \\ -6[15] + 46 = a_n \\ -90 + 46 = a_n \\ -44 = a_n[/tex]
Use the Arithmetic Sequence to figure this out.
I am joyous to assist you anytime.
Calculate a6 for the geometric sequence in which a1=1500 and the common ratio is 3/5.
Answer:
The sum would be a₅ = 506.25!
Step-by-step explanation:
Given that,
first term a₁ = 1600
common ratio (r) =
We need to find the fifth term of the geometric progression
We know that the nth term formula
aₙ = a₁rⁿ-¹
where a₁ is first term and r is the common ratio
n is the number of terms
So, n = 5
a₅ = 1600
a₅ = 1600*
a₅ = 1600*81/256
a₅ =
a₅ = 506.25
Answer:
116.64
Step-by-step explanation:
116.64 is the correct answer
when a1 = 1500 the a6 = 116,64
Write a numerical expression that represents the number of increments it will take to reach -60 feet.
Answer:
Step-by-step explanation:
Write a numerical expression that represents the number of increments it will take to reach -60 feet
Answer:
(-60) ÷ (-10)
Step-by-step explanation:
Jenni wrote a rational number that is positive. Which of the following is not a possible number that she wrote?
51/4
0
7/8
1
Answer:
There is no answer.
0 is rational since it can be written as a fraction (0/5, 0/69)
1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25
what is the formula for the nth term of the given sequence?
3, 5, 7...
What is the scale factor and length of side x
Answer:
The scale factor is 2
x=11 units
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The ratio of its corresponding sides is called the scale factor
In this problem
Triangles RST and MNO are similar
so
[tex]\frac{NO}{ST}=\frac{MN}{RS}[/tex]
substitute the given values
[tex]\frac{x}{5.5}=\frac{6}{3}[/tex]
solve for x
[tex]\frac{x}{5.5}=2[/tex]
[tex]x=2(5.5)\\x=11\ units[/tex]
The scale factor of triangle RST to triangle MNO (enlargement) is equal to 2
if sec thita . sin thita =0,then find the value of thita
Answer:
[tex]\large\boxed{\theta=k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sec\thets\cdot\sin\theta=0\iff \sec\theta=0\ \vee\ \sin\theta=0\\\\\sec\theta\neq0\ \text{for any value of}\ \theta\\\\\sin\theta=0\Rightarrow\theta=k\pi\ \text{where}\ k\in\mathbb{Z}[/tex]
B is the midpoint of AC. If: AB = 9x+1 and BC= 6x+25 Find AC
Answer:
AC = 146
Step-by-step explanation:
Given that B is the midpoint of AC, then
AB = BC, that is
9x + 1 = 6x + 25 ( subtract 6x from both sides )
3x + 1 = 25 ( subtract 1 from both sides )
3x = 24 ( divide both sides by 3 )
x = 8
Hence
AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus
AC = (15 × 8) + 26 = 120 + 26 = 146
Answer:
146
Step-by-step explanation:
AB = BC (Definition of midpoint) so:
9x+1=6x+25.
Solve it as you would any other algebraic equation >>> 9x+1=6x+25 >>> 9x+1-1=6x+25-1 >>> 9x=6x+24 >>> -6x+9x=6x-6x+24 >>> 3x=24 >>> 3x/3=24/3 >>> x=8
AB=9x+1 >>> AB=9*8+1 >>> AB=73
BC=6x+25 >>> BC=6*8+25 >>> BC=73
AC=AB+BC >>> AC=73+73 >>> AC=146
What is the y-intercept of f(x)=8x^5-3x^3+12
The y intercept is (0, 12)
Solution:
Given function is:
[tex]f(x) = 8x^5 - 3x^3 + 12[/tex]
To find: y intercept
y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y
Substitute x = 0 in given function
[tex]f(0) = 8(0) -3(0) + 12[/tex]
y = 0 - 0 + 12
y = 12
Thus y - intercept is (0, 12)
The mass of two sacks of potatoes is 168 grams. One-eight of the mass of Sack A and three-quarter of the mass of Sack B is 76 grams. Write an equation to find the mass of Sack A.
Answer:
1/8(A)+(3/4)(168-A)=76 is an equation to find the mass of A, the mass of A is 80 grams.
Step-by-step explanation:
What do we know?
Both sacks together are 168 grams. Therefore;
A+B=168
One eighth of sack A and three quarters of sack B is equal to 76 grams. Therefore;
1/8(A)+(3/4)B=76
Let's solve using the substitution method to find A. First, we need to isolate and then substitute B for an expression containing A.
A+B=168
B=168-A
Now that we have isolated B, we can substitute '160-A' for B in the other equation.
1/8(A)+(3/4)(168-A)=76
1/8(A)-3/4(A)+126=76
1/8(A)-3/4(A)+126=-50
-5/8(A)=-50
A=80
which expression is equivalent to 2m+m+m
3m
4m
2m^3
4m^3
Answer:
4m
Step-by-step explanation:
since it is not multiplication, there would be no power.
think of it as 2m + 1m + 1m
The answer is 4m
I hope this helped! If so, please mark brainliest!
given: <1 and <2 and supplements, <3 and <4 are supplements, and <1 ≅ <4
prove: <2 ≅ <3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Step-by-step explanation:
The supplementary angles are:
Two angles their sum is 180°The supplement of an acute angle is an obtuse angle and vice versaThe supplement of a right angle is a right angleIf one angle is supplement to two other angles, then the two angles are equal in measure (if 50° is supplement to angles X and Y, then X and y must be 130°)Supplement angles of congruent angles are congruent (If angles X and Y are supplement to angles A , B and angles A , B are congruent, then angles X and Y are congruent∵ ∠1 and ∠2 are supplementary
∴ m∠1 + m∠2 = 180° ⇒ (1)
∵ ∠3 and ∠4 are supplementary
∴ m∠3 + m∠4 = 180° ⇒ (2)
We can equate the left hand sides of (1) and (2) because the right hand sides are equal
∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)
∵ ∠1 ≅ ∠4
∴ m∠1 = m∠4
- Substitute m∠4 by m∠1 in (3)
∴ m∠1 + m∠2 = m∠3 + m∠1
- Subtract m∠1 from both sides
∴ m∠2 = m∠3
∴ ∠2 ≅ ∠3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Learn more:
You can learn more about supplementary angles in brainly.com/question/10483199
#LearnwithBrainly
Lin is saving $300 per year in an account that pays 4.5% interest per year, compounded annually. How do I find the value after 20 years?
To find the value after 20 years, use the future value of a series formula with the given parameters, resulting in an approximate amount of $9,321.
Explanation:To find the value of $300 saved annually at 4.5% interest compounded annually after 20 years, we use the future value of a series formula:
FV = [tex]P * ((1 + r)^n - 1) / r[/tex]
Where:
FV = Future value of the seriesP = Yearly deposit ($300)r = Annual interest rate (4.5% or 0.045)n = Number of years (20)Substituting the given values:
FV = $300 * ((1 + 0.045)^20 - 1) / 0.045
= $300 * ((1.045)^20 - 1) / 0.045
= $300 * (2.398 - 1) / 0.045
= $300 * 1.398 / 0.045
= $300 * 31.07
= $9,321
Therefore, after 20 years, the value will be approximately $9,321.
4. Solve this equation: Y/g + 5 = 0.
O A. y = 5
O B.y=-5
O C.y=-45
O D. y = 45
Answer:
C) Y = -45
Step-by-step explanation:
Y/9 + 5 = 0
Y/9 = -5
y = -5 * 9
Y= -45
in trapezium abcd, as shown in the figure, ab is parallel to dc, ad=dc=bc=20cm and ‹a=60°. find: (i) length of ab (ii) distance between ab and dc
Answer:
AB = 40 cm
Distance = [tex]10\sqrt{3}[/tex] cm
Step-by-step explanation:
Draw two heights DE and CF. These heights together with bases of trapezoid form rectangle DEFC. In this rectangle, DC=EF=20 cm.
Consider right triangle ADE. In this triangle, angle ADE has the measure of 30° (the sum of the measures of all interior angles is always 180°, so m∠ADE=180°-60°-90°=30°)
Leg opposite to 30° angle is equal to half of the hypotenuse, so
[tex]AE=\dfrac{1}{2}AD=\dfrac{1}{2}\cdot 20=10\ cm[/tex]
Similarly, in triangle CBF, BF=10 cm.
Hence,
[tex]AB=AE+EF+FB=10+20+10=40\ cm[/tex]
The height of the trapezoid (the second leg of triangle ADE) is the distance between DC and AB. By the Pythagorean theorem,
[tex]AD^2=AE^2+DE^2\\ \\DE^2=20^2-10^2=400-100=300\\ \\DE=\sqrt{300}=10\sqrt{3}\ cm[/tex]
Assume that the quadrilateral shown is a parallelogram. Which expression represents the area of the parallelogram?
Answer:
B. x² + 16x + 15
Step-by-step explanation:
Area of parallelogram = base x height
A = (x + 15) (x + 1) = x² + 16x + 15
Paul and Cindy own different pizza shops. Paul makes 12 pizzas the first day and 6 pizzas each day after that. Cindy makes 16 pizzas the first day and 4 pizzas each day after that. Who will have made more pizzas after 9 days? How many pizzas will that person have made?
A . Paul. He has made 80 pizzas after 9 days.
B . Cindy. She has made 132 pizzas after 9 days.
C. Paul. He has made 60 pizzas after 9 days.
D . Cindy. She has made 48 pizzas after 9 days.
Answer:
Paul. He has made 60 pizzas after 9 days.
Step-by-step explanation:
Paul makes 12 pizzas the first day and 6 pizzas each day after that.
So, after 9 days Paul will make total [12 + (9 - 1)6] = 60 pizzas.
Now, Cindy makes 16 pizzas the first day and 4 pizzas each day after that.
So, after 9 days Cindy will make total [16 + (9 - 1)4] = 48 pizzas.
Therefore, after 9 days Paul will make more pizzas and the number is 60 pizzas. (Answer)
Answer:
B
Step-by-step explanation:
Find the median. Round to the nearest tenth if necessary.
49, 13.9, 5.9, 16.6, 43.1, 11.2, 36.8, 43.7, 22.9, 45.1, 44.2
Answer:
The median refer to the middle
value or number when arranged ascendingly or descendingly therefore the MEDIAN IS 36.8
Step-by-step explanation:
By arranging the numbers ascendingly we have
5.9, 11.2, 13.9, 16.6, 22.9, 36.8, 43.1, 43.7, 44.2, 45.1, 49
Therefore the median which is the number at the centre is 36.8
The equation d = d equals StartFraction m Over V EndFraction. can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?
Answer:
m/d = V
Step-by-step explanation:
Answer:
m/d=V
Step-by-step explanation:
I did the quiz
Aramp is 17 feet long, rises 8 feet above the floor, and covers a horizontal distance of 15 feet, as shown in the figure.
The ratio of
is equal to tan B.
The ratio of the vertical rise to the horizontal distance on the ramp is equal to tan B.
Explanation:The given figure represents a ramp with a length of 17 feet, rising 8 feet above the floor, and covering a horizontal distance of 15 feet. To find the ratio of the vertical rise to the horizontal distance (tan B), we can use the trigonometric function tangent (tan).
Tan B = vertical rise / horizontal distance = 8 feet / 15 feet = 0.5333
evaluate √7x(√x-7√7
pls & thanks!
Answer:
[tex]x\sqrt{7} - 49\sqrt{x}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}\sqrt{7x}(\sqrt{x} - 7\sqrt{7}) & = & \sqrt{7x}\times\sqrt{x}- 7\sqrt{7}\times\sqrt{7x} \\ & = & \sqrt{7}\times\sqrt{x}\times\sqrt{x} - 7\sqrt{7}\times\sqrt{7}\times\sqrt{x}\\& = & \sqrt{7}\times x - 7\times 7\times\sqrt{x}\\& = &\mathbf{ x\sqrt{7} - 49\sqrt{x}}\\\end{array}[/tex]
An online retailer charges $6.99 plus $0.55 per pound to ship electronics purchases. How many pounds is a DVD player for which the shipping charge is $11.94?
Answer:
[tex]9\ pounds[/tex]
Step-by-step explanation:
Let
x ----> the number of pounds of a DVD player
we know that
The number of pounds of a DVD player multiplied by the cost per pound ($0.55) plus the charge of $6.99 must be equal to $11.94
so
The linear equation that represent this situation is
[tex]0.55x+6.99=11.94[/tex]
solve for x
subtract 6.99 both sides
[tex]0.55x=11.94-6.99[/tex]
[tex]0.55x=4.95[/tex]
divide by 0.55 both sides
[tex]x=9\ pounds[/tex]
10 POINTS!!! will give Brainliest
Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
The volume of the prism will be given by 204.7 cubic cm.
Step-by-step explanation:
The area of a triangle whose three side lengths are given is equal to
Δ = [tex]\sqrt{s(s - a)(s - b)(s - c))}[/tex] .......... (1)
Where, a, b, and c are the three side lengths and s is the half perimeter i.e.
[tex]s = \frac{a + b + c}{2}[/tex] ......... (2)
Now, in our case, [tex]s = \frac{6 + 7 + 6}{2} = 9.5[/tex] {From equation (2)}
So, Δ = [tex]\sqrt{9.5(9.5 - 6)(9.5 - 7)(9.5 - 6)} = 17.05[/tex] sq. cm.
{From equation (1)}
Hence, the volume of the prism will be given by (17.05 × 12) = 204.7 cubic cm. (Answer)
I am three years younger than my brother, and I am 2 years older than my sister. My mom age is one less than three times my brothers age . When you add all our you get 87. What are our pages ?
Answer:
The "I" figure is 13 years old. Her brother is 16. Her Sister is 11. Her mother is 47.
Step-by-step explanation:
13+16=29
29+11=40
40+47=87
Are the fractions 3/9, 3/10, 3/11, and 3/12 in order from least to greatest
Answer:
The fractions [tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex] are not in order from least to greatest.
Step-by-step explanation:
Given order of fractions from least to greatest:
[tex]\frac{3}{9},\frac{3}{10},\frac{3}{11},\frac{3}{12}[/tex]
To check if the fractions are in correct order.
Solution:
The fractions given have same numerators but different denominators.
For fractions the higher the denominator the lower is the value of that fraction.
Thus, in the given list the least value fraction will be the fraction with the greatest denominator which is [tex]\frac{3}{12}[/tex] and the greatest value fraction will be the fraction with the least denominator which is [tex]\frac{3}{9}[/tex]
So, the order of the fractions from least to greatest is not correct. Instead the order is from greatest to least.
The correct order from least to greatest should be:
[tex]\frac{3}{12},\frac{3}{11},\frac{3}{10},\frac{3}{9}[/tex].
trapizoid figure STUV is scaled version of figure WXYZ. The scale factor of figure STUV to figure WXYZ is 3:1. If ST= 117 mm and SV= 153 mm, what is the length of side WZ?
Answer:
39mm
Step-by-step explanation:
Final answer:
Using the scale factor of 3:1, the length of side WZ from trapezoid WXYZ can be calculated by dividing the known length of side SV from trapezoid STUV by the scale factor. The length of WZ is found to be 51 mm.
Explanation:
If trapezoid STUV is a scaled version of trapezoid WXYZ with a scale factor of 3:1, we can use this scale factor to determine the length of side WZ given the lengths of ST and SV. To find the length of WZ, we divide the length of SV by the scale factor. Since SV = 153 mm and the scale factor is 3, we perform the division 153 mm / 3 to get 51 mm as the length of WZ.
A proportion is a mathematical statement that two ratios or fractions are equal. It is used to express the equality of two fractions that compare two numbers or quantities to each other. For example, if we have two fractions a/b and c/d, a proportion states that these two fractions are equivalent: a/b = c/d. Proportions are fundamental in various branches of mathematics and applications, including solving problems involving scales, maps, and ratios in real-life scenarios.
Mary says 1/8 is
greater than 1/4 because 8 is greater than 4.
Is Mary's reasoning correct? Explain.
Answer:
No, Mary is incorrect. If you turn the fractions into decimals, 1/4 would be 0.25 and 1/8 would be 0.12½. Since 0.25 is greater than 0.12½, Mary is incorrect.
Mary's reasoning is incorrect because in fractions, the larger the denominator, the smaller the fraction's value, making 1/4 greater than 1/8.
Mary's reasoning that 1/8 is greater than 1/4 because 8 is greater than 4 is not correct. In the context of fractions, the larger the denominator (the bottom number), the smaller each part of the whole it represents. Thus, 1/4 is actually greater than 1/8 because dividing something into 4 parts results in larger parts than dividing it into 8 parts. This can be further understood by transforming both fractions into equivalent fractions with a common denominator or by converting them into decimal form (0.25 for 1/4 and 0.125 for 1/8) to directly compare their sizes.
Find the indicated probability. Round to three decimal places. The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked? 0.006 0.033 0.027 0.032
Answer:
0.033
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
Here, p = 0.5, q = 0.5, and n = 11.
We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.
r = 0:
P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰
P ≈ 0.0005
r = 1:
P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹
P ≈ 0.0054
r = 2:
P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²
P ≈ 0.0269
Therefore, the total probability is:
P = 0.0005 + 0.0054 + 0.0269
P = 0.0328
Round to the thousandths place, the probability is 0.033.
Mrs. Kelly creates a garden. She buys 15 flowers and 3 bushes for a total cost of $160.32. Each bush costs $11.50 more than each flower. How much does each bush cost?
The cost of each bush is $ 18.49
Solution:Let "f" be the cost of each flower
Let "b" be the cost of each bush
Given that Mrs. Kelly buys 15 flowers and 3 bushes for a total cost of $160.32
15 flowers x cost of each flower + 3 bushes x cost of each bush = 160.32
[tex]15 \times f + 3 \times b = 160.32[/tex]
15f + 3b = 160.32 ----- eqn 1
Each bush costs $11.50 more than each flower
Cost of each bush = 11.50 + cost of each flower
b = 11.50 + f ------ eqn 2
Let us solve eqn 1 and eqn 2 to find values of "b" and "f"
Substitute eqn 2 in eqn 1
15f + 3(11.50 + f) = 160.32
15f + 34.5 + 3f = 160.32
18f = 160.32 - 34.5
18f = 125.82
f = 6.99Substitute f = 6.99 in eqn 2
b = 11.50 + 6.99 = 18.49
b = 18.49Thus the cost of each bush is $ 18.49
Ms. Fuller has 2 2/6 pies left over from her party. Write the number of pies left over as a fraction greater than 1.
Answer:
[tex]\frac{14}{6}[/tex]
Step-by-step explanation:
A mixed fraction of the form [tex]a\frac{b}{c}[/tex] can be converted into an improper fraction by writing it in the form [tex]\frac{(ac)+b}{c}[/tex] . By applying this formula , we can see that [tex]2\frac{2}{6} = \frac{12 +2}{6} =\frac{14}{6}[/tex] . As numerator is greater than the denominator , we can see that the answer is greater than one and thus it is an improper fraction.
Create an equation where the solutions are 1/3 and 4 plus or minus i sqrt 7
Answer:
[tex] 3 {x}^{3} - 25 {x}^{2} + 35x - 23 = 0[/tex]
Step-by-step explanation:
We want to create an equation that will have the solution
[tex]x = \frac{1}{3},x = 4 + \sqrt{7}i,x = 4 - \sqrt{7}i[/tex]
This implies that:
[tex]3x -1= 0,x -( 4 + \sqrt{7}i) = 0,x - ( 4 - \sqrt{7}i) = 0[/tex]
We put the roots in factored form by reversing the zero product principle to get:
[tex](3x -1)(x -( 4 + \sqrt{7}i))(x - ( 4 - \sqrt{7}i)) = 0[/tex]
We expand the last two parenthesis to get:
[tex](3x - 1)( {x}^{2} - 4x + \sqrt{7}ix - 4x - \sqrt{7}ix + 16 - 7 {i}^{2}) = 0 [/tex]
We simplify to get:
[tex](3x - 1)( {x}^{2} - 8x + 23) = 0[/tex]
We expand further to obtain:
[tex]3 {x}^{3} - 25 {x}^{2} +35x - 23 = 0[/tex]