Answer: 1547 bricks are required to build the staircase.
Step-by-step explanation:
We are given:
Number of bricks in the first step, [tex]a_1[/tex] = 131
Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126
Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121
Sequence become:
131, 126, 121, .....
These are in arithmetic progression where a = 131 and d (common difference) = -5
To calculate the sum of an AP, we use the formula:
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
where,
n = number of terms = 17
Putting values in above equation, we get:
[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]
Hence, 1547 bricks are required to build the staircase.
Point A has coordinates (-24, -54)
Point B has coordinates (40, -46)
Find the equation of the perpendicular bisector of line AB.
ANSWER ASAP
Answer:
[tex]y=-8x+14[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
A perpendicular bisector of a line segment is 1) perpendicular to the line segment and 2) passes through the midpoint of the line segmentPerpendicular lines always have slopes that are negative reciprocals (ex. -2 and 1/2)Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of when x is 0)1) Determine the midpoint of the line segment
Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where the coordinates of the endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the endpoints (-24, -54) and (40, -46)
[tex](\frac{-24+40}{2} ,\frac{-54+(-46)}{2} )\\(\frac{-24+40}{2} ,\frac{-54-46}{2} )\\(\frac{16}{2} ,\frac{-100}{2} )\\(8 ,-50)[/tex]
Therefore, the midpoint of line AB is (8,-50).
2) Determine the slope of the line segment
This will help us find the equation of the perpendicular bisector.
slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the endpoints (-24, -54) and (40, -46)
[tex]= \frac{-46-(-54)}{40-(-24)}\\= \frac{-46+54}{40+24}\\= \frac{8}{64}\\= \frac{1}{8}[/tex]
Therefore, the slope of line AB is [tex]\frac{1}{8}[/tex].
3) Determine the slope of the perpendicular bisector
Because perpendicular lines always have slopes that are negative reciprocals, the slope of the perpendicular bisector is -8 (the negative reciprocal of 1/8). Plug this slope into [tex]y=mx+b[/tex]:
[tex]y=-8x+b[/tex]
4) Determine the y-intercept (b) of the perpendicular bisector
[tex]y=-8x+b[/tex]
Recall that we found the midpoint of line AB, (8,-50). The perpendicular bisector passes through this point. Plug (8,-50) into [tex]y=-8x+b[/tex] and solve for b:
[tex]-50=-8(8)+b\\-50=-64+b[/tex]
Add 64 to both sides to isolate b
[tex]-50+64=-64+b+64\\14=b[/tex]
Therefore, the y-intercept of the line is 14. Plug this back into [tex]y=-8x+b[/tex]:
[tex]y=-8x+14[/tex]
I hope this helps!
Assume that in a statistics class the probability of receiving a grade of A equals .30 and the probability of receiving a grade of B equals .30. The probability that a randomly selected student from this class will receive either an A or a B equals:________
a. 0.09
b. 9
c. 6
d. 3
Answer:
c. 0.6
Step-by-step explanation:
A student cannot receive an A or a B simultaneously, so [tex]P(A \cap B) = 0[/tex].
Grade of A equals .30 and the probability of receiving a grade of B equals .30.
This means that [tex]P(A) = P(B) = 0.3[/tex]
The probability that a randomly selected student from this class will receive either an A or a B equals:
This is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.3 + 0.3 - 0 = 0.6[/tex]
So the probability is 0.6, and the correct answer is given by option c.
Help! 3-4 quick please!!
To complete a task in 30 days a company needs
4 people each working for 7 hours per day.
The company decides to have
5 people each working for 6 hours per day.
Assuming that each person works at the same rate,
how many days will the task take to complete?
Answer:
28 days
Step-by-step explanation:
4 x 7 x 30= 840 total working hours
5 x 6 x n = 840
= n = 840 ÷ 30
= n = 28 days
The task will take approximately 1 day to complete with 5 people working for 6 hours per day.
Determining the time to complete the taskTotal work done in the first scenario = 4 × 7 × 30
= 840 work hours
Total work done in the second scenario = (5 × 6 × D)
= 4 × 7 × 30
Solving for D:
30D = (4 × 7 × 30) / (5 × 6)
D = (4 × 7) / (5 × 6)
D = 28 / 30
D ≈ 0.9333
Rounding up to the nearest whole day, D = 1
Therefore, the task will take approximately 1 day to complete with 5 people working for 6 hours per day.
Learn more on time calculation here https://brainly.com/question/26046491
Answer the following: a) 2x32 =
b) (2 x 3)2 =
Answer:
a) 64 b) 12
Step-by-step explanation:
32 + 32 = 64
2*3 = 6
6*2 = 12
Answer:
a) 64 b) 12
Step-by-step explanation:
The answer for a is simple the answer is 64 just multipy 32 with 2 and the second one first you have to solve he answer iin the bracket then the answer you get from the bracket you will have to multiply with the number outside the bracket which is 2 and the answer you get will be 12.
As a nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patient's doctor indicated that you should mix 100 milligrams of Medication A with 80 milligrams of Medication B. However this week, the doctor said to only use 16 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
Answer:
Step-by-step explanation:
20 milligrams
Find the selling price of a $32 item after a 50% markup.
The selling price is $
Answer:
The new price is 48
Step-by-step explanation:
First find the markup
50% of 32
.5 * 32 = 16
Add the markup to the original price
16+32 = 48
The new price is 48
Answer:
$48
Step-by-step explanation:
32 * 0.50 = 16
32 + 16 = 48
Hope this is helpful
Which of the quadratic functions has the narrowest graph?
y = 2x^2
y = –x^2
y = 1/8x^2
y = 1/6x^2
A quadratic function's graph being wide or narrow is determined or depended on a-term:
[tex] \large{y = a {x}^{2} + bx + c}[/tex]
If |a| has a lot of value, for example a = 2 or a = 100. The graph will get narrower if increasing the value of |a|. On the other hand, If |a| has small value, for example a = 1/2 or a = 1/10000. The graph would be wide.
Also it does not matter if a-term is negative or not since a-term being positive or negative determines if a parabola is upward or downward. Only |a| determines how narrow/wide the graph is.
From the question, it is clear that the parabola y = 2x^2 is the narrowest graph since it has the highest |a| value out of all choices.
Answer
y = 2x^2The weights of a certain dog breed are approximately normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds. Use your graphing calculator to answer the following questions. Write your answers in percent form.
Required:
a. Find the percentage of dogs of this breed that weigh less than 53 pounds.
b. Find the percentage of dogs of this breed that weigh less than 49 pounds.
c. Find the percentage of dogs of this breed that weigh more than 49 pounds.
Answer:
a. 74.86%
b. 50%
c. 50%
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds.
This means that [tex]\mu = 49, \sigma = 6[/tex]
a. Find the percentage of dogs of this breed that weigh less than 53 pounds.
The proportion is the p-value of Z when X = 53. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{53 - 49}{6}[/tex]
[tex]Z = 0.67[/tex]
[tex]Z = 0.67[/tex] has a p-value of 0.7486.
0.7486*100% = 74.86%, which is percentage of dogs of this breed that weigh less than 53 pounds.
b. Find the percentage of dogs of this breed that weigh less than 49 pounds.
p-value of Z when X = 49, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 49}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5
0.5 = 50% of dogs of this breed that weigh less than 49 pounds.
c. Find the percentage of dogs of this breed that weigh more than 49 pounds.
1 subtracted by the p-value of Z when X = 49, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{49 - 49}{6}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a p-value of 0.5.
1 - 0.5 = 0.5 = 50% of dogs of this breed that weigh more than 49 pounds.
write an equation for the line parallel to y=-3x+4 that contains P(1,4)
Answer:
y = -3x + 7
Step-by-step explanation:
If the line is parallel, it will have the same slope. So, this line will have a slope of -3.
Plug in the slope and given point into y = mx + b, and solve for b:
y = mx + b
4 = -3(1) + b
4 = -3 + b
7 = b
Plug in the slope and y intercept into y = mx + b
y = mx + b
y = -3x + 7
So, the equation is y = -3x + 7
question 7.
identify the zeros of the graphed function
A) -2,2
B)-2,0,2
C)-2
D)2
Answer:
-2,0 0,-8 , 2,0 hope that helps
Gerald is thinking of a number n, and he wants his sister to guess the number. His first clue is that 7 more than 3 times his
number is at least 10 and at most 28. Write a compound inequality that shows the range of numbers that Isabella might be
thinking of.
Write your answer in interval notation. For example-3
Answer:
(1, 7)
Step-by-step explanation:
The number is n.
7 more than 3 times his
number is at least 10 and at most 28.
Thus;
10 ≤ 3n + 7 ≤ 28
Let's solve individually;
10 ≤ 3n + 7
10 - 7 ≤ 3n
n ≥ 3/3
n ≥ 1
Also,
3n + 7 ≤ 28
3n ≤ 28 - 7
3n ≤ 21
n ≤ 21/3
n ≤ 7
Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;
(1, 7)
Written as a simplified polynomial in standard form, what is the result when
(2x + 4)^2 is subtracted from 7x^2-10x-10?
At the start of a month, Sasha and Natalia each have a certain amount of money.
Sasha has $400 and saves $20 each week. The graph below shows the amount of money in Natalia's account each week
Whose monthly activity shows a greater rate of change, and by how much?
A) Sasha, by $10/week
B)Sasha, by $19/week
C) Natalia, by $10/week
D) Natalia, by $19/week
Answer:
Option (A)
Step-by-step explanation:
Sasha has an amount of $400 and saves $20 per week.
If we graph the savings of Sasha, her savings per week will be defined by the slope of the line = $20 per week
Similarly, from the graph attached,
Slope of the line given in the graph = Per week savings of Natalia
Slope of line passing through (0, 190) and (2, 210) will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{210-190}{2-0}[/tex]
= 10
Therefore, per week savings of Natalia = $10
Difference in savings of Sasha and Natalia = 20 - 10 = $10 per week
Here, Sasha shows the greater rate of change by $10 per week
Therefore, Option (A) will be the answer.
a number is 2 more than 3 times the other number if the is 26 then the number are
Answer:
80
Step-by-step explanation:
more in math means add
if you multiply three by 26 is 78 + 2 would be 80
PSA im not great in math
Raj is travelling to another country.
He flies for 5 hours at an average speed of 950 km/h on one plane.
He then flies for 6 hours 30 minutes at an average speed of 830 km/h on a second plane.
What is the total distance, in km, he travelled by plane?
Answer:
10145
Step-by-step explanation:
5 times 950 equals 4750
and 6.5 times 830 equals 5395
add first and second value
4750 + 5395 equals 10145
there is no arguing
Answer:
10145 km
Step-by-step explanation:
Time x speed = Distance
5 x 950 = 4750
6.5 x 830 = 5395
add together = 10145
Seven-eighths of the 360 adults attending a school bazaar were relatives of the students. How many attendees were not relatives?
Answer:
45
Step-by-step explanation:
If 7/8 are relatives, 1/8 are not relatives
360 / 8 = 45
What is the best estimate of the perimeter of the figure on the grid if each square has side lengths of 1 mm?
Answer:
the ans of this question is 30cm².
Which of the following is next in the series
Answer:
a
Step-by-step explanation:
blue red blue red like this
HELPPPPPPPPPPPP PLEASEEEEEEEEEEE I NEEEEEDDDDDDDD HELP IM BEGGING SOMEONE PLEASEEEEEEEEEEEE
Answer:
49.13
Step-by-step explanation:
1/2×6×8=24 3.14×4²/2=23.15
24+23.15=49.13
3p + 7q = 55
7p + 7q = 91
What is p and q
Step-by-step explanation:
3p + 7q = 55
7p + 7q = 91
(-)
-4p=-36
p=9
q=4
Answer:
p = 9 and q = 4
Step-by-step explanation:
3p + 7q = 55 -- (1)
7p + 7q = 91 -- (2)
(2) - (1) : 4p = 36
p = 9 -- (3)
Substituting (3) into (1),
27 + 7q = 55
7q = 28
q = 4 -- (4)
Therefore, p = 9 and q = 4
If this helps you, please mark brainliest!
Have a nice day!
Find the value of 100-98+96-94+92-90+...+8-6+4-2
Answer:
10
solution
100-98 =2
96-94 = 2
92-90 = 2
8-6 = 2
4-2 =2
2+2+2+2+2=10✓
3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.
3.) If y varies directly as x and y = 24 when x = 6, find the variation constant and the equation of variation.
Solution:-A. Express the statement “y varies directly as x”, as y = kx .
B. Solve for k by substituting the given values in the equation.
[tex]\sf\rightarrow{y = kx}[/tex]
[tex]\sf\rightarrow{24 = 6k}[/tex]
[tex]\sf\rightarrow{K = \frac{24}{6} }[/tex]
[tex]\sf\rightarrow{K={\color{magenta}{4}}}[/tex]
Answer:-Therefore, the constant of variation is 4.C. Form the equation of the variation by substituting 4 in the statement y = kx. Thus , y = 4 x.
[tex]{\large{—————————————————————}}[/tex]
#CarryOnMath⸙
Zoe draws ABC on the coordinate plane.
ТУ
B
5
4
3
2.
1
А
ol
1
12
13
4
5
What is the approximate perimeter of AABC to the nearest hundredth?
O A 8.47 units
o
B
12 units
C 12.94 units
O D. 15.31 units
Answer:
12.94 units
Step-by-step explanation:
Perimeter of ∆ABC = AB + BC + AC
✔️Distance between A(1, 1) and B(3, 5):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] A(1, 1) = (x_1, y_1) [/tex]
[tex] B(3, 5) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(3 - 1)^2 + (5 - 1)^2} [/tex]
[tex] AB = \sqrt{(2)^2 + (4)^2} [/tex]
[tex] AB = \sqrt{4 + 16} [/tex]
[tex] AB = \sqrt{20} [/tex]
AB = 4.47 units
✔️Distance between B(3, 5) and C(5, 1)
[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Where,
[tex] B(3, 5) = (x_1, y_1) [/tex]
[tex] C(5, 1) = (x_2, y_2) [/tex]
[tex] BC = \sqrt{(5 - 3)^2 + (1 - 5)^2} [/tex]
[tex] BC = \sqrt{(2)^2 + (-4)^2} [/tex]
[tex] BC = \sqrt{4 + 16} [/tex]
[tex] BC = \sqrt{20} [/tex]
BC = 4.47 units
✔️Distance between A(1, 1) and C(5, 1):
AC = |1 - 5| = 4 units
✅Perimeter of ∆ABC = 4.47 + 4.47 + 4 = 12.94 units
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = 1 + 2√t, y = t3 - t, z = t3 + t; (3,0,2)
Solution :
Given parametric equation for :
[tex]$x=1+2 \sqrt t$[/tex]
[tex]$y=t^3-t$[/tex]
[tex]z=t^3+t[/tex]
The point is (3, 0, 2)
The vector equation is equal to :
[tex]$r(t) = \left<1+2 \sqrt t, t^3 -t, t^3+t \right>$[/tex]
Solving for r'(t) by differentiating each of the components of r(t) w.r.t. to t,
[tex]$r'(t)= \left< \frac{1}{\sqrt t}, \ 3t^2-1, \ 3t^2+1 \right>$[/tex]
The parameter value corresponding to (3, 0, 2) is t = 1. Putting in t=1 into r'(t) to solve for r'(t), we get
[tex]$r'(1) = \left< \frac{1}{\sqrt 1}, \ 3(1)^2-1, \ 3(1)^2+1 \right>$[/tex]
We know that parametric equation for line through the point [tex]$(x_0, y_0, z_0)$[/tex] and parallel to the direction vector <a, b, c > are
[tex]$x=x_0+at$[/tex]
[tex]$y=y_0+bt$[/tex]
[tex]z=z_0+ct[/tex]
Now substituting the [tex]$(x_0, y_0, z_0)$[/tex] = (3, 0, 2) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get:
[tex]$x=3+(1)t$[/tex]
x = 3 + t
y = (0) + (2)t
y = 2t
z = (2) + (4)t
z = 2 + 4t
a garden pond is in the shape of a rectangle that measures 5 m by 3 m. a stone path is built all around the pond. this path is the same width all the way around. the area of the pond and the path together is 39 m². how wide is the path?
Answer:
1.16 m (approximately)
Step-by-step explanation:
Let x be the width of the path.
Total area = (5+2x)(3+2x) = 39
Expand and simplify
4x²+ 16x+15-39 = 0
4x² + 16x - 24 = 0
Simplify
x² + 4x -6 = 0
Rational factoring does not work, so use quadratic formula
x = +/- sqrt(10) -2
= 1.16 or -5.16 (reject)
= 1.16 m (approximately)
If a obtuse triangle Has a base of 9in an 13in height what is the area triangle?
Lin is reading a 47-page book. She read the first 20 pages in 35 minutes.
If she continues to read at the same rate, will she be able to complete this book in under 1 hour?
[ Select ]
If so, how much time will she have left? If not, how much more time is needed?
[ Select ]
Answer:
no
22.25 minutes
Step-by-step explanation:
First determine how long it will take her to read the entire book
20 pages 47 pages
-------------- = ----------------
35 minutes x minutes
Using cross products
20x = 35*47
20x=1645
Divide by 20
20x/20 = 1645/20
x =82.25 minutes
This is more than 1 hour ( 1 hour = 60 minutes)
82.25 minutes - 60 minutes = 22.25 minutes
She will need 22.25 more minutes
Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The length of side Y X is 9 centimeters.
The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Select two options.
YZ = 9 cm
XZ = 9 cm
XZ = 9 StartRoot 2 EndRoot cm
XZ = 2(XY)
YZ is the longest segment in △XYZ.
The side YZ=9 cm of the right angle
We have given that,
Triangle X Y Z is shown. Angle X Y Z is a right angle and angles Y Z X and Z X Y are 45 degrees. The length of side Y X is 9 centimeters.
The length of segment XY is 9 cm.
We have to determine the statements regarding triangle XYZ are correct.
What is the right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular.
The right angle with angles 45-45-90 has two side same.
Therefore the side YZ=9 cm bc of the right angle
To learn more about the right-angle triangle visit:
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#SPJ5
Can you solve this problem
Answer:
x = 18
Step-by-step explanation:
8 x 18 - 3 = 141