Answer:
[tex]13x=39[/tex]
Step-by-step explanation:
Given
[tex]2x - y = -4 \to 10x - 5y =-20[/tex]
[tex]3x +5y =59 \to 3x +5y = 59[/tex]
Required
What can replace [tex]3x +5y = 59[/tex] ?
We have:
[tex]10x - 5y =-20[/tex]
and
[tex]3x +5y = 59[/tex]
Add up both equations:
[tex]10x +3x-5y+5y=-20+59[/tex]
[tex]10x +3x=39[/tex]
[tex]13x=39[/tex]
Since [tex]13x=39[/tex] is a result of [tex]10x - 5y =-20[/tex] and [tex]3x +5y = 59[/tex],
[tex]13x=39[/tex] can replace [tex]10x +3x=39[/tex]
Suppose that a randomly generated list of numbers from 0 to 9 is being used
to simulate an event that has a probability of success of 80%. Which of these
groups of numbers could represent a success?
A. 0, 1, 2, 3, 4, 5, 6, 7, 8
B. 0, 1, 2, 3, 4, 5
C.0, 1, 2, 3, 4, 5, 6, 7
D. 0, 1, 2, 3, 4, 5, 6
========================================================
Explanation:
There are 7 numbers in the set {1,2,...,6,7}. Then we add on 0 to get to the 8th number. So there are 8 numbers overall listed in bold above.
Since the sample space is {0,1,2,...,8,9}, we have 10 digits listed here. So the probability of success is 8/10 = 0.80 = 80%
Side note: The values 8 and 9 would represent a failure. We have 2 failures out of 10 so we get 2/10 = 0.20 = 20%
The groups of numbers could represent a success 80 percent is {0, 1, 2, 3, 4, 5, 6, 7}. Therefore, option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.
Here, the sample space is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
To simulate an event that has a probability of success of 80%.
Now, 8/10 ×100
= 8×10
= 80%
Therefore, option C is the correct answer.
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Matthew was assigned 234 math problems over the weekend. He completed five times as many problems on Saturday than Sunday. How many math problems did Matthew solve on Saturday?
Answer:
[tex]195[/tex]
Step-by-step explanation:
Let [tex]a[/tex] represent the number of math problems Matthew solved on Sunday. From the problem, we know he solved [tex]5a[/tex] problems on Saturday.
Therefore, we have:
[tex]5a+a=234,\\6a=234,\\a=39[/tex]
Substitute [tex]a=39[/tex] into [tex]5a[/tex]:
[tex]5(39)=\boxed{195}[/tex]
Toby ran a 10-kilometer race in
1 hours. Which point on the number
line represents his time?
Answer:
Point S
Step-by-step explanation:
Given that :
Time taken = 1 2/5 hours
Converting to decimal :
1 2/5 = 7/5 = 1.40 hours
From the number line, distance between each successive tick mark represents, 0.05 hours :
Hence, the point which depicts Toby's time on the number line is: point S
I need help...........
Answer:
4
Step-by-step explanation:
Break down the shape into a rectangle and a triangle
To find the base of the triangle subtract
(3x-1)-(x+1)= 2x-2
which means the area of the triangle is
.5(2x-2)(x-1)= x²-2x+1
Let's then find the area of the rectangle
(x+1)(x-1)= x²-1
Take the sum and set this equal to 40
(x²-2x+1)+(x²-1)=40
simplify...
2x²-2x-40=0
x²-x-20=0
(x-5)(x+4)=0
Reject the negative answer and get x=5
Then it's just a matter of plugging in x=5 for the height (x-1)
5-1=4 which is the final answer
Answer:
4 cm.
Step-by-step explanation:
Area formulas:
A(Rectangle) = bh
A(Triangle) = 1/2bh
A(Trapezium) = A(Rectangle) + A(Triangle)
Use the information given and substitute the values to solve for the missing height:
A(Rectangle) + A(Triangle) = A(Trapezium)
bh + 1/2bh = 40
(x + 1)(x - 1) + 1/2(2x - 2)(x - 1) = 40
x² - 1 + x² - 2x + 1 = 40
2x² - 2x = 40
2x² - 2x - 40 = 0
Use Quadratic Formula to solve for x:
a = 2, b = -2, c = -40
x = (-b ± √(b² - 4ac))/2a
x = (-(-2) ± √((-2)² - 4(2)(-40)))/2(2)
x = (2 ± 18)/4
x = 5 and x = -4
Since we cannot have a negative height, we use x = 5:
h = (5) - 1 = 4
Therefore, the height of the trapezium is 4 cm.
how to find the area of triangle?
Answer:
[tex](i). \\ { \tt{area = 2(\frac{1}{2} \times base \times height}} )\\ = 4 \times 3 \\ = 12 \: sq \: units \\ \\ (iii). \\ = \frac{1}{2} \times 8 \times 6 \\ = 24 \: sq \: units \\ \\ (ii). \\ = \frac{1}{2} \times 12 \times 5 \\ = 30 \: sq \: units[/tex]
Bal Bharti Vidyalaya is located in the Karauli district of Rajasthan. The school decided to go for a plantation drive for 2 days on the occasion of Vanmahotsava. The Principal of the Vidyalaya asked the forest department to provide plants. It was decided that each student has to plant an equal number of trees on both days. On the first day, all the participants planted 5 trees each. The number of boys and girls who participated was in the ratio 5:4. (i) If the number of trees planted by the students on the first day was 5400, how many boys participated? [1] (ii) Find the total number of students who participated in this program? [1] (iii) If the total number of trees planted on the second day was 7560, then how many trees were planted by each one of them
Answer:
i). 600 Boys
ii). 1080 Students
iii). 7 Trees each students On Second day
Step-by-step explanation:
According to the Question,
Given, Bal Bharti Vidyalaya is located in the Karauli district of Rajasthan. The school decided to go for a plantation drive for 2 days on the occasion of Vanmahotsava. The Principal of the Vidyalaya asked the forest department to provide plants. It was decided that each student has to plant an equal number of trees on both days. On the first day, all the participants planted 5 trees each. .The number of boys and girls who participated was in the ratio of 5x:4x.i). If the number of trees planted by the students on the first day was 5400.
We Know, Each Student Has Planted 5 Plants on First day So, Girls And Boys Ratio are 5x : 4x , Thus Total Students Are 9x .NOw, This 9x Planted 9x × 5 ⇒ 45x Trees on First Day.
45x = 5400 ⇔ x=120
So, The Number Of Boys Are 5x = 5 * 120 ⇒ 600Boys
And, The Number of Girls Are 4x = 4 * 120 ⇒ 480Girls
ii). the total number of students who participated in this program is 600 boys + 480 Girls = 1080 Students.
iii). If the total number of trees planted on the second day was 7560. We Know Every Student Plant Equal Number Of trees on each day.
So, 1080 Students Planted 7560 Plants
Therefor, each Student Planted 7560/1080 = 7 Trees Each On Second day.
pls help me solve pls show how you got the answer
Answer:
A
Step-by-step explanation:
270/9=30
42, 43, 44, 44, 49, 40, 39
What is the mean?
Answer:
43
Step-by-step explanation:
To find the mean, add up all the numbers
(42+ 43+ 44+ 44+ 49+ 40+ 39)=
301
Then divide by the number of terms
301/7
43
Answer:
mean = 43
Step-by-step explanation:
Mean is given by
mean = sum of all numbers / total no. of terms
substitute the values
mean = 42 + 43 + 44 + 44 + 49 + 40 + 39 /
Divide ,
mean = 301 / 7
mean = 43
Which statement about the angles in the figure is true?
mZ3+ m25 = 180°
mZ1 + m28 = 90°
m28+ m29 = 90°
m27 +mZ10 = 180°
Answer:
the second one
Step-by-step explanation:
its the sum oh 90
The length of the base of an isosceles triangle is x. The length of a leg is 3x−7. The perimeter of the triangle is 77. Find x.
Answer the question in the picture
Answer:
(10^3)^2
Hope this answer is right!!
Step-by-step explanation:
(10^3)^2
(10)^3*2
(10)^5
A video game has a wheel that turns one degree every time the figure pops a ballon then figure has popped 40 balloons how many degrees has the wheel turned?
A teacher has 40 learners in her class. She chooses 1% to clean her board. Is this possible?
Step-by-step explanation:
No, 1% of 40 is the same as 40% of 1. Which is 0.025% You cant have 0.025% of a learner or a human so this isn't possible.
Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the left.
A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3 and a bold line starts at negative 3 and is pointing to the right.
Answer:
3 < x
Step-by-step explanation:
3(8 – 4x) < 6(x – 5)
Divide each side by 3
3/3(8 – 4x) < 6/3(x – 5)
(8 – 4x) < 2(x – 5)
Distribute
8-4x < 2x-10
Add 4x to each side
8-4x+4x < 2x-10+4x
8 < 6x-10
Add 10 to each side
8+10 < 6x-10+10
18 < 6x
Divide by 6
18/6 < 6x/6
3 < x
Mary took 8 tests in science and received the following scores: 87,60,76,92,63,91,88,75
Answers:
mean = 79mode = nonemedian = 81.5=================================================
Explanation:
To get the mean, you add up the numbers and then divide by n = 8, since there are 8 scores
Adding the scores gets us: 87+60+76+92+63+91+88+75 = 632
Divide that over n = 8 to get 632/n = 632/8 = 79
The mean is 79
You have the correct answer. Nice work.
---------------
The mode is the most frequent value.
In this data set, we don't have any repeated values. Each unique number is listed one time only. So that tells us we don't have a mode here.
---------------
To get the median, we need to sort the items from smallest to largest
{87,60,76,92,63,91,88,75} sorts to {60,63,75,76,87,88,91,92}
Because we have n = 8 values, which is an even number, this tells us that the median is between slot n/2 = 8/2 = 4 and slot 5
The values 76,87 are in slots four and five in that order. Add them up and divide by 2: (76+87)/2 = 163/2 = 81.5 is the median
My son wants to celebrate his birthday at the bowling alley with a few of his friends. He has $70 to spend. The bowling alley charges a flat fee of $40 for a private party and $4.50 per person for shoe rentals and unlimited bowling.
The maximum number of people he can pay for at the bowling alley is __.
Answer: he can pay for 6 people total (including him)
Step-by-step explanation:
first lets subtract the flat fee from the total amount of money he has
70 - 40 = 30
now lets divide 30 by $4.50 to see how many people he can pay for
30 / $4.50 = about 6.5
obviously you cant pay for half a person so he can invite 5 people (he also has to pay for himself)
Answer:
6 people
Step-by-step explanation:
Why would there be a difference between percentages with the Empirical Rule and the actual percentages?
Answer:
Given that [tex]\int\limits^a_b {\frac{1}{2\pi } e^{-1/2} x} \, dx[/tex] is not the easiest equation to solve, and that
the values at the convenient ± 1 sigma,± 2 sigma,± 3 sigma are irrational
using the "rule-of-thumb" "empirical rule" is typically "close enough"
given that the whole probability analysis by definition has some uncertainty in it
Step-by-step explanation:
The percentages of a normal distribution data lies within three standard deviations of its mean for empirical rule while it's definite for actual percentages.
What is the empirical rule?The empirical rule is also referred to as the 68-95-99.7 rule and it can be defined as a rule in statistics which states that:
The middle 68% of a normal distribution would be within one standard deviation of its mean (µ ± σ).The middle 95% of a normal distribution would be within two standard deviations of its mean (µ ± 2σ).The middle 99.7% of a normal distribution would be within three standard deviations of its mean (µ ± 3σ).In Statistics, there is a difference between percentages calculated by using the empirical rule and the actual percentages because a normal distribution data lies within three standard deviations of its mean for the former but it is definite for the latter.
In conclusion, the empirical rule is more important to researchers and statistician because it can be used to determine outcomes and gain insight even when all the data aren't available.
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Using the quotient rule, what is the derivative of the function f(x)=(3x-5)/(5x+2)?
Answer:
[tex]\frac{31}{(5x+2)^2}[/tex]
Step-by-step explanation:
See image for quotient rule
f(x)= numerator = 3x-5
g(x)= denominator = 5x+2
so we have
[tex]\frac{(5x+2)(3x-5)'-(3x-5)(5x+2)'}{(5x+2)^2}\\(3x-5)'=3\\(5x+2)'=5\\\frac{(5x+2)(3)-(3x-5)(5)}{(5x+2)^2}\\\frac{15x+6-(15x-25)}{(5x+2)^2}\\\frac{31}{(5x+2)^2}[/tex]
(5a + 2)(a + 4) =
(Answer should be a polynomial in standard form.
Answer:
(5a+2)(a+4)
=5a^2+20a+2a+8
=5a^2+22a+8
Answer:
[tex]5 {a}^{2} + 22a + 8[/tex]
Step-by-step explanation:
[tex](5a + 2)(a + 4) \\ 5a(a + 4) + 2(a + 4) \\ 5 {a}^{2} + 20a + 2a + 8 \\ 5 {a}^{2} + 22a + 8 \\ [/tex]
If g(x) = x^2 - 3, find the value of:
a) g(5)
b) g(-2)
c) g(a+1)
Answer:
this answer kajjsnnsnsnsnsnsnsnsnssnnsnssnjxxjxnxnxxnndnsndnsndndnd
Answer
g(5)=22
g(-2)=1
g(a+1)=(a+1)^2-3
g(a+1)= (a+1)(a+1)-3
g(a+1)=a^2+2a-2
Step-by-step explanation:
if you wanted to solve for a you would need to use the quadratic formula and solve for a.
Question 3 of 10
of the way from
What is the location of the point on the number line that is
A = 5 to B = 23?
O
A. 8
B. 9
C. 10
D. 7
Answer:
B. 9
Step-by-step explanation:
solve it and u will find out
What is the area is square feet?
Answer:
A = 24
Step-by-step explanation:
Figure shown is a trapezoid
Area of a trapezoid = [tex]\frac{a+b}{2} h[/tex]
where a and b = base lengths and h = height
The trapezoid shown has the following dimensions
Shorter base length (a) = 6
Longer base length (b) = 10
Height (h) = 3
Using these dimensions , plug in the values into the area formula
A = [tex]\frac{6+10}{2} 3[/tex]
add 6 + 10 = 16
[tex]A=\frac{16}{2} 3[/tex]
divide 16/2 = 8
[tex]A = (8)(3)[/tex]
multiply 8 times 3
A = 24
During a sale, a store offered a 20% discount on a stereo system that originally sold for $320. After the sale, the discounted price of the stereo system was marked up by 20%.
Answer:
354 $ is correct
Step-by-step explanation:
your v id dead
Math help please show work thanks
Problem 3
If we peel off the sticker off the side of a 3D cylinder, then we can form a rectangle (imagine we're able to peel it off completely without any folds or tears).
The length of the rectangular sticker is the distance around the curved circular base. So it's C = pi*d = pi*1.5 = 1.5pi inches across. The height of the rectangle is the same as the height of the cylinder. So the height is 5 inches.
The area of the rectangle is: length*width = (1.5pi)*(5) = 7.5pi
That's the exact area in terms of pi
If you use the approximation pi = 3.14, then we'll get 7.5*3.14 = 23.55 square inches as the final answer
==================================================
Problem 4
The square base has area of 38*38 = 1444 square cm
The side panels are 4 identical triangles. Each triangle has area base*height/2 = 38*55/2 = 1045 square cm. Meaning that all four triangles combine to a lateral surface area of 4*1045 = 4180 sq cm.
The total surface area is: 1444+4180 = 5624 square cm.
When you wrote 55*38*2+38*38 on your paper, you had the right idea because that evaluates to 5624
What is the slope that passes through the points (-9.-8) (-15,-16)
Answer:
Slope/gradient is 4/3
Step-by-step explanation:
Have a nice day
Find the ratio of sin (A)
Answer:
sin (A) = 8/17
Step-by-step explanation:
Sine = opposite/hypotenuse
Sin (A) = 16/34
Sin (A) = 8/17
Answer:
sin (A) = 16/34
Step-by-step explanation:
SOH (sine = opposite/adjacent)
Someone plss help me on this one too!
Thanks :)
Answer: 30%
Step-by-step explanation:
Which of the following equations
has - 4 as a
as a possible value of p
Answer:
You need to add the eqautions
Step-by-step explanation:
What additional information could be used to prove AABC = AMQR using SAS? Select two options.
Answer:
To prove that ΔABC ≅ ΔMQR using SAS, we show that two sides with the intersection angle are congruent. From the diagram, it is shown that CA is congruent to RM. From the first option, given that m∠A = 64° and AB = MQ = 31 cm, then we have CA = RM, AB = MQ, and CAB = RMQ (i.e. m∠A = m∠M = 64°).
The pair of triangles below have two corresponding parts marked as congruent. What additional information is
needed for a HL congruence correspondence?
A. ∠M≅∠H
B. LM≅JK
C. LM≅JH
D. LN≅JK
(there is a line above the letters besides a)
Answer:
C. LM ≅ JH
Step-by-step explanation:
The criteria that needs to be satisfied before two right triangles can be said to be congruent to each other is by the Hypotenuse-Leg Theorem are:
1. Both must have a corresponding leg that are congruent to each other.
In the diagram given above, NM is congruent to KH. They are corresponding legs that are congruent.
2. The hypotenuse of one triangle must be equal to that of the other.
We are not given if the hypotenuse of one, LM is congruent to the hypotenuse of the other, JH.
Therefore, the additional information required would be:
LM ≅ JH