Answer:
f(-1) = -1
Step-by-step explanation:
f(x) = -x^2
Let x = -1
f(-1) = - ( -1) ^2
= -1
Find the sum of each finite series. Σ⁵ n=1(2 n-1)
The sum of the given finite series is 25
The summation notation means that we have to add the terms of the given series with n moves from the lower limit to the upper limit.
The given series is:
[tex]\sum\limits^5_{n=1} {(2n-1)}[/tex]
In this series, the lower limit is n = 1 while the upper limit is n=5.
n = 1 ⇒ 2n - 1 = 2(1) -1 = 1
n = 2 ⇒ 2n - 1 = 2(2) -1 = 3
n = 3 ⇒ 2n - 1 = 2(3) -1 = 5
n = 4 ⇒ 2n - 1 = 2(4) -1 = 7
n = 5 ⇒ 2n - 1 = 2(5) -1 = 9
Hence,
[tex]\sum\limits^5_{n=1} {(2n-1)}=1+3+5+7+9[/tex]
We can evaluate the sum of the series directly, or by using the sum formula as follow:
S(n) = n/2 [a(1) + a(n)]
Substitute n = 5, a(1) =1, and a(n) = 9:
S(5) = 5/2 (1 + 9) = 25
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A baby weighs 20 pounds at her four-month appointment. Six months later, she weighs 24 pounds. By what percentage did the baby's weight increase? 22% 15% 25% 20%
The weight of the baby increased by a 20%
By what percentage did the baby's weight increase?We know that the initial weight of the baby is 20 pounds, so that will be our 100%, and we can write:
20lb = 100%
Then the weight is 24 lb, so that will represent another percentage X, we can write:
24lb = X
We can solve this for X, taking the quotient between the relations:
(24lb/20lb) = X/100%
(24lb/20lb)*100% = X = 120%
So we can see that the weight of the baby increased by a 20%
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Solve the equation.
100 t=70 /240
The solution of t in 100 t=70 /240 is t= 7/2400
How to solve the equation?The equation is given as
100 t=70 /240
Divide both sides of the equation by 100
So, we have
t=70 /240 * 1/100
Evaluate
t= 7/2400
Hence, the solution of t in 100 t=70 /240 is t= 7/2400
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The women's 400m world record is 42.60 seconds. the 16th fastest women's 400m runner ran it in 49.24 seconds. what time is exactly halfway between these two times?
The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.
Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.
If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.
n = (42.60 + 49.24)/2
n = 91.84/2
n = 45.92 seconds
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At a football game half time show, the marching band was in 3 sections, each with 8 rows of 8 players. The dancers were in 2 sections each with 6 rows of 7 dancers. What is the total number of band members and dancers in the halftime show?
The total number of band members and dancers in the halftime show in all rows were 276.
What is a row?A row is an arrangement of things in a straight line next to each other.
if there are n rows and each row has m members then total number of members = m* n
Given that marching band was in 3 sections and each section has 8 rows of 8 players , then players in each section of marching band = 8 *8 = 64
As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192
Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.
Then, dancers in each section of dancers = 6*7 =42
As there are two such sections, then the total dancers = 2* 42 = 84
total no of band members and dancers = 192+84 = 276
Therefore, The total number of band members and dancers in the halftime show were 276.
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Directions:Add. Express The answer in simplest form. show all necessary work -2 2/3 - 7 1/3
Answer:
-10
Step-by-step explanation:
Convert to improper fractions and do the math
-8/3 - 22/3
-30/3
-10
solve 2xy - x = 3for y. Then find the value for y when x=2
solve 2y + xy = 6for y. Then find the value of y when x= -3
Answer:
1) y=5/4
2) y=−6
Step-by-step explanation:
Let's solve the equation step by step.
1) 2xy - x = 3
(2)(2)y - 2 = 3
4y - 2 = 3
4y−2=3
Step 1: Add 2 to both sides.
4y−2+2=3+2
4y=5
Step 2: Divide both sides by 4.
4y/4 = 5/4
y=5/4
2) 2y + xy = 6
2y−3y=6
Step 1: Simplify both sides of the equation.
2y−3y=6
2y+−3y=6
(2y+−3y)=6(Combine Like Terms)
−y=6
−y=6
Step 2: Divide both sides by -1.
−y/−1 = 6/−1
y=−6
9th Grade Math - Geometry
Given: B is the midpoint of AC.
C is the midpoint of BD.
Prove AB = CD
Answer in two-column proof format, please.
If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.
Given that B is midpoint of AC and C is the midpoint of BD.
We are required to prove that AB is equal to CD.
Midpoint is the point which divides the line segment into two equal parts.
If B is midpoint of AC then,
2AB=AC-----1
2BC=AC-----2
If C is midpoint of BD then,
2BC=BD-----3
2CD=BD-----4
From 1 & 2
2AB=2BC
AB=BC
Put the value of BC from 3.
AB=BD/2
Now put the value of BD from 4.
AB=2CD/2
AB=CD
Hence proved
Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.
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1. A study is made to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration # 1, the reaction was run 15 times with an average velocity of 7. 5 micromoles per minutes and a standard deviation of 1. 5 with a substrate concentration #2, 12 runs were made, yielding an average velocity of 8. 8 micromoles per minutes and a sample standard deviation of 1. 2. Is there any reason to believe concentration #2 causes an increase in the mean velocity over concentration #1? use 0-0. 05 level of significance and assume the populations to be approximately normal distribution with equal variance. Instructions 1. Hypothesis.
There is not enough evidence
What is standard deviation ?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.
For 1.5 moles substrate concentration per liter
Reaction ( n2 ) = 15 runs
average velocity ( x2 ) = 7.5 micromoles per 30 minutes
standard deviation ( s2 ) = 1.5
For 2.0 moles substrate concentration per liter
Reaction( n1 ) = 12 runs
(x1) = 8.8 micromoles on average per 30 minutes
standard deviation ( s1 ) = 1.2
Show Reason to believe that this increase in substrate conc causes an increase in mean velocity
Hypothesis test
H0 : μ1 - μ2 = 0.5
H1 : μ1 - μ2 > 0.5
significance level ( ∝) = 0.01
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What is the value of the digit in the thousands place?
5,963
OA. 900
OB. 300
O C. 5
OD. 5,000
Answer: D
Step-by-step explanation:
explicit rule 26,18,10,2
[tex]Answer:\ a_n=34-8n[/tex]
Step-by-step explanation:
26, 18, 10, 2
18-26=-8
10-18=-8
2-10=-8
This is an arithmetic progression:
[tex]a_n=a_1+(n-1)d,\\a_1=26\ \ \ \ \ d=-8\ \ \ \ n=1,\ 2,\ 3,\ 4\\a_n=26+(n-1)(-8)\\a_n=26+(n)(-8)+(-1)(-8)\\a_n=26-8n+8\\a_n=34-8n[/tex]
If a voltage of 110 V is applied across a
load and the resulting current flow is 2.2 A,
what is the resistance of the load in Ohms
Answer:
50 ohms.
Step-by-step explanation:
Volts = current * resistance
110 = 2.2 * r
R = 110 / 2.2
= 50 ohms.
Oscar wants to rent a boat. Boats 4 Less charges a fee of $100 and $35 per hour after that. Boats-R-Us doesn't charge a fee but charges $50 per hour. If Oscar wants to rent the boat for 8 hours, which rental company should he use and why?
(P.S. This has to do with Linear Equations so figure out which form to use Point-Slope From, Slope Intercept Form or Standard Form)
The rental company to hat Oscar should use is the second company because it's cheaper.
How to illustrate the information?The total amount charged for the first boat will be:
= 100 + 35h
where h = number of hours
= 100 + 35(8)
= 100 + 260
= $360
The amount charged for the second company will be:
= 50 × 8
= 400
Therefore, the rental company to hat Oscar should use is the second company because it's cheaper.
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COORDINATE GEOMETRY Find the measures of the sides of ΔJ K L and classify each triangle by the measures of its sides. (Lesson 4-1)
J(-7,10), K(15,0), L(-2,-1)
ΔJKL has 53.28 units of side length.
What is a triangle's definition?A triangle is a polygon with three sides and three edges.It is a fundamental geometric shape.Triangle ABC is a three-vertical triangle with the letters A, B, and C on each side.Any three non-collinear points define a unique triangle and, by extension, a unique plane in Euclidean geometry.So,
The formula for the perimeter of the side of a triangle: √(x₂−x₁)²+(y₂−y₁)²
Filling the values in the formula, we obtain:
= √(15−(-7))²+(0−10)²= 53.28 unitsThen, each side of the triangle will be: 53.28 units
Therefore, ΔJKL has 53.28 units of side length.
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Choose an equation for the relationship between the measures of the angles and arcs.
1 and the intercepted arcs and ________.
m1 = (m + m)
m1 = (m - m)
m1 = m + m
The expression that relates the measure of <1 and arcs QP and arcSP is expressed as m<1 = 1/2(arcQR+arcSP)
Circle theoremWhen two chords intersect inside a circle, the angle formed is half of the sum of the subtended arcs.
From the given diagram, the intercepted arcs are arcQR and arcSP and the measure of the interior angle is <1.
Using the theorem above, the expression that relates the measure of <1 and arcs QP and arcSP is expressed as:
m<1 = 1/2(arcQR+arcSP)
The measure of the angle <1 is equivalent to half the sum of arcQR and arcSP.
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Given point B is between A and C, where AC = 27 and AB = 10, What is BC?
Answer: BC=17
Step-by-step explanation:
AC=AB+BC
27=10+BC
27-10=10-10+BC
BC=27-10
BC=17
3n-21=2n (2-step equations)
Answer:
n=21
Step-by-step explanation:
3n-21=2n
subtract 3n from each side
-21=-1n
two negatives become a positive
Type the correct answer in the box. Use numerals instead of words.The graphs of functions fand g are shown.Function g is defined as g(x)
= k f(x). What is the value of K?
Answer:
k = 1
This is because when g(x) = 8, f(x) = 8
and when g(x) = 2, f(x) = 2
and this continues throughout the graph
Brian has $24 worth of pizza delivered to his house. He pays the bill plus a 15% tip and 7% sales tax. He also pays a 3$ delivery fee that is charged after the tax and tip how much change does he receive, if he pays with two $20 bills?
Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.
Given that,
Pizza costing $24 is being delivered to Brian's home.
He pays the amount in addition to the 7% sales tax and 15% tip.
In addition, he pays the delivery price of $3, which is added on after tax and tip.
We have to find how much change does he get if he uses two $20 bills as payment.
To figure out the sales tax
$24×0.07=$1.68
To figure out the tip
$24×0.15=$3.6
The Total cost=$24+$1.68+$3.6+$3=$32.28
Now, To find change we have to add the Total cost and the bill
Change=2($20)-$32.28
Change=40-32.28
Change=$7.72
Therefore, The change $7.72 he get if he uses two $20 bills as payment.
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The angle adjacent to ∠ C is called an exterior angle of triangle A B C . Make a conjecture about the relationship among ∠A, ∠ B , and the exterior angle at C .
Here the conjecture we can made is :
The sum of interior angles i.e. ∠A and ∠B is equal to the exterior angle at C.
What is external and internal angles ?The exterior angle of any triangle is defined as the angle which is at the outside boundaries of that triangle. whereas, the interior angle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle for that triangle.
What is adjacent angle ?In mathematics, the two angles are called as adjacent angles if they have a common vertex or we can say they are angle of a common vertex in the triangle.
we can define the adjacent angle as the angles which have common side and common vertex and they don't overlap.
Exterior angle PropertyAccording to the exterior angle property, if a side of a triangle is made, then the exterior angle formed is always equals to the sum of two interior angles opposite to each other in the triangle.
Thus on the basis of exterior angle property we can make the conjecture that, "the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles".
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Helen Mountain Tubing charges $25 for tube rental and $5 an hour to float down the river. Alpine Tubing charges $30 for tube rental and $2 an hour to float down the river. Create an equation to determine at what point the cost of both tubing companies is the same.
25x - 5 = 30x - 2
25x + 5 = 30x + 2
25 + 5x = 30 + 2x
25 - 5x = 30 + 2x
Answer:
25 + 5x = 30 + 2x
At 5/3s of an hour is when the cost of both tubing companies are the same.
This is when the price of both companies both hit $33.33
Step-by-step explanation:
25 + 5x = 30 + 2x
move variables by subtracting
25 + 3x = 30
move constants by subtracting
30 - 25 = 5
5 = 3x
x = 5/3
If £2000 is placed into a ban account that pays 3% compound interest per year how much will be in the account after 2 years
Answer:
There is 2121.80 in the account after 2 years.
Step-by-step explanation:
Use the formula A = P(1 + r)^t where P = initial amount, A = amount after t years and r = the rate (as a decimal).
So, for this problem:
Amount after 2 years = 2000(1 + 0.03)^2
= £2121.80
The cost of playing pool increases with the amount of time using the table. Identify the independent and dependent quantity I'm the situation
Solve for x.
-3/8x-7/24x+1/3x=-40
Answer:
120
Step-by-step explanation:
We start with the equation:
[tex]\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40[/tex]
We need to set the fractions into equal denominations so we can sum them all together:
[tex]\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\[/tex]
Now sum the fractions:
[tex]\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40[/tex]
Multiple both sides by 24 to eliminate denominator on left side of equation:
[tex]-8x=-960[/tex]
Divide both sides by -8 to get the value of x:
[tex]x=120[/tex]
Find the measure of the missing angles
Answer: d=90 degrees
e=69 degrees
f=111 degrees
Step-by-step explanation:
69+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.
69-69+f=180-69
f=180-69
f=111 degrees
e+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.
e+111=180
e+111-111=180-111
e=180-111
e=69 degrees
d+90=180 ==> if there is a tiny box between an angle, that means that the angle is a right angle which measures 90 degrees.
d-90+90=180-90
d=180-90
d=90 degrees
HELP FAST i'll mark you brainliest please.
The transformation of the given function g(x) = ¹/₂|x + 4| - 3 using the format h(x) = a|bx + c| + d, gives;
a = ¹/₂
b = -1
c = 6
d = 3
How to carry out Transformation of functions?
We are given the function;
g(x) = ¹/₂|x + 4| - 3
Now, we are told that the function is first translated by 6 units upwards, and so this means a transformation of;
g(x) + 6 = ¹/₂|x + 4| - 3 + 6
g'(x) = ¹/₂|x + 4| + 3
Now, we are told that it now undergoes a transformation of 2 units to the right, this gives;
g"(x) = ¹/₂|x + 4 + 2| + 3
g"(x) = ¹/₂|x + 6| + 3
Finally, after undergoing a transformation of reflection in the y-axis, we have; h(x) = ¹/₂|-x + 6| + 3
For the format of;
h(x) = a|bx + c| + d, it means that we have;
a = ¹/₂
b = -1
c = 6
d = 3
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pls help, I need this ASAP, brainliest to the person with solution and right answer
Answer:
see explanation
Step-by-step explanation:
1
(5p² - 3) + (2p² - 3p³) ← remove parenthesis
= 5p² - 3 + 2p² - 3p³ ( collect like terms , largest exponent first )
= - 3p³ + 7p² - 3
2
(a³ - 2a²) - ( 3a² - 4a³) ← distribute second parenthesis by - 1
= a³ - 2a² - 3a² + 4a³ ( collect like terms, largest exponent first )
= 5a³ - 5a²
3
(- 4[tex]k^{4}[/tex] + 14 + 3k²) + (- 3[tex]k^{4}[/tex] - 14k² - 8) ← remove parenthesis
= - 4[tex]k^{4}[/tex] + 14 + 3k² - 3[tex]k^{4}[/tex] - 14k² - 8 ← collect like terms, largest exponent first
= - 7[tex]k^{4}[/tex] - 11k² + 6
4
(3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex]) - (- 6[tex]n^{4}[/tex] - 3n - 8[tex]n^{5}[/tex]) ← distribute second parenthesis by - 1
= 3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex] + 6[tex]n^{4}[/tex] + 3n + 8[tex]n^{5}[/tex] ( collect like terms, largest exponent first )
= 2[tex]n^{5}[/tex] - 2[tex]n^{4}[/tex] + 3n + 3
5
(y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex]) + (- 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] ) - ( [tex]x^{4}[/tex]y³ + 6[tex]x^{4}[/tex][tex]y^{4}[/tex])
remove parenthesis from first 2 and distribute third by - 1
= y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] - [tex]x^{4}[/tex]y³ - 6[tex]x^{4}[/tex][tex]y^{4}[/tex]
collect like terms
note the term with the largest exponent is [tex]x^{4}[/tex][tex]y^{4}[/tex]
= (- 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 6[tex]x^{4}[/tex][tex]y^{4}[/tex] ) + (- 10[tex]x^{4}[/tex]y³ - [tex]x^{4}[/tex]y³) + (y³ + 6y³)
= - 13[tex]x^{4}[/tex][tex]y^{4}[/tex] - 11[tex]x^{4}[/tex]y³ + 7y³
Find the missing term(s) of each arithmetic sequence. 1, □, 9,. . . . .
Missing term i.e., the second term of the sequence is 5.
As the series is in an arithmetic sequence, so we have an equation
[tex]a_{n}[/tex] = a +(n-1)d
Where a = first number of the series
n = number of term
d= common difference
As we know the 3rd term of the sequence, so by this we can find the common difference.
So we have,
9 = 1 +(3-1)d
8=2d
d=4
common difference = 4
Now we have to find the 2nd term or the missing term of the sequence, so we have
[tex]a_{2}[/tex] = 1 +(2-1)4
= 1+ 1×4
= 1+4
= 5
Therefore the 2nd term is 5.
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in a test designed to assess small motor coordination, kindergarten pupils are timed on their performance of a specific task. it is known that the time required to complete the task has an approximate bell-shaped distribution with mean 36 seconds and a standard deviation (s.d.) of 6 seconds. how long should the test administrator allow for the performance of the task, if it is desired that approximately 97.5% of the kindergarten pupils complete the task? question 16 options: 30 42 24 48
It would take the test administrator 48 seconds to allow for the performance of the task
So, if we want 97.5 percent, we must look it up in our z table. So I need to find the z score that is closest to.975, which is 1.96.
The 97.5th percentile point of the standard normal distribution is a quantity often used in probability and statistics for statistical computations. This figure is around 1.96, which means that 95% of the area under a normal curve is within 1.96 standard deviations of the mean.
As a result, the z score for the 97.5th percentile would be multiplied by the class standard deviation. As a result, we obtain;
1.96*6 = 11.76
Then, this new time gotten would be added to the first mean of the class,
As a result, we have 36+11.76 = 47.76 which is approximately 48
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Evaluate each expression 10+8^3 divid 16
Answer:
42
Step-by-step explanation:
= 10+8^3/16
= 10+512/16
= 10+32
= 42
