Answer:
The number of sweets in the 10th bag is 53
Step-by-step explanation:
Given
Let the Number of sweets in a bag be represented by x and frequency be represented by f
The table is as follows
x F
39 1
40 2
41 5
42 0
43 1
Mean = 42
Required
How many sweets are in the 10th bag?
Represent the number of sweets in the 10th bag by y;
The table becomes
x F
39 1
40 2
41 5
42 0
43 1
y 1
The mean of observation is calculated using the following formula;
Mean = ∑fx/∑f
Where ∑ means summation
fx means f * x; i.e. product of frequency and number of sweets
f represents frequency;
Calculating ∑fx
∑fx = 39 * 1 + 40 * 2 + 41 * 5 + 42 * 0 + 43 * 1 + y * 1
∑fx = 39 + 80+ 205 + 0 + 43 + y
∑fx = 367 + y
Calcuating ∑f
∑f = 1 + 2 + 5 + 0 + 1 + 1
∑f = 10
Recall that
Mean = ∑fx/∑f and Mean = 42;
So, Mean = ∑fx/∑f becomes
[tex]42 = \frac{367 + y}{10}[/tex]
Multiply both sides by 10
[tex]42 * 10 = \frac{367 + y}{10} * 10[/tex]
[tex]420 = 367 + y[/tex]
Subtract 367 from both sides
[tex]420 - 367= 367 -367 + y[/tex]
[tex]53 = y[/tex]
[tex]y = 53[/tex]
Hence, the number of sweets in the 10th bag is 53
The total number of sweets in the 10th bag is 53 and this can be determined by using the formula of the mean.
Given :
The total number of bags is 10.The mean number of sweets in the bags is 42.The table shows how many sweets there are in 9 of the bags.The following steps can be used in order to determine the total number of sweets in the 10th bag:
Step 1 - The formula of the mean can be used in order to determine the total number of sweets in the 10th bag.
Step 2 - The formula of mean is given below:
[tex]{\rm Mean}= \dfrac{\sum f \times x}{\sum f}[/tex]
Step 3 - Now, substitute the values of the known terms from the given table in the above expression.
[tex]{\rm Mean}= \dfrac{39 \times 1+40 \times 2+41 \times 5+42 \times 0+43 \times 1+y \times 1}{1+2+5+0+1+1}[/tex]
Step 4 - Simplify the above expression.
[tex]\begin{aligned}\\42&= \dfrac{367+y }{10}\\y &=53 \\\end{aligned}[/tex]
So, the total number of sweets in the 10th bag is 53.
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3.
Which of the following points lie on the x-axis?
(A) (3,4)
(B) (7,0)
(C) (0,8)
(D) (-9,0)
(F) (-3,-5)
Answer:
D and B is the answer
Step-by-step explanation:
Here is a graph with the points
solve the equation x square - 9+20=0
Answer:
[tex]\sqrt{11i}[/tex]
Step-by-step explanation:
x^2-9+20 = 0
x^2+11 = 0
x^2 = -11
x = [tex]\sqrt{-11} \\\sqrt{11i} \\[/tex]
Need help please help me
Answer:
0.000000207 in scientific notation = 2.07 × 10^-7
Remember it has to have one number before the decimal.
8.2 * 10^-7 in standard form = 0.00000082
YOu have to move the decimal back.
In the first box the answer is 2.07 × 10^-7.
In the second box the answer is 0.00000082.
The complex solution to a quadratic equation is below. Write this solution in standard form, a+bi, where a and b are real numbers. What are the values of a and b.
Answer:
a = -6 and b = 3√2
Step-by-step explanation:
Given the complex solution below;
x = (-24±√-288)/4
Re writing in the standard format a,+bi
x =( -24±√144×√2×√-1)/4
In complex notation, i = √-1
x = (-24±√144×√2×i)/4
x = ( -24±12×√2i)/4
x = -24/4±12√2i/4
x = -6±3√2i
Comparing the resulting complex number with a+bi
a = -6 and b = 3√2
How do I complete this formal check?
Answer:
Step-by-step explanation:
The first two steps are for the purpose of eliminating fractions. Doing so results in 4(2x - 5) = 9(x - 2), which is to be solved for x.
Perform the indicated multiplication, obtaining:
8x - 20 = 9x - 18.
Then combine like terms: -2 = x, or
x = -2.
To complete the formal check, substitute -2 for x in the first equation. This results in:
(1/3)(-4 - 5) = (3/4)(-2 -2), or
-3 = -3
... which is obviously true.
what is the definition for congruent arcs
Answer:
"If two arcs are both equal in measure and they're segments of congruent circles, then they're congruent arcs"
Step-by-step explanation:
Please help! Correct answer only!
For a fundraiser, there is a raffle with 100 tickets. One ticket will win a $150 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
$ ___
Answer:
Expected Payoff ⇒ $ 1.50 ; Type in 1.50
Step-by-step explanation:
Considering that 1 out of the 100 tickets will have a probability of winning a 150 dollar prize, take a proportionality into account;
[tex]100 - Number of Tickets,\\1 - Number of Tickets You Can Enter,\\\\1 / 100 - Probability of Winning,\\$ 150 - Money Won,\\\\Proportionality - 1 / 100 = x / 150, where x - " Expected Payoff "\\\\1 / 100 = x / 150,\\100 * x = 150,\\\\Conclusion ; x = 1.5 dollars[/tex]
Thus, Solution ; Expected Payoff ⇒ $ 1.50
En un colegio hay dos grupos de 1º ESO con 24 alumnos cada uno.
a) Si las chicas de 1º A son el doble que los chicos, ¿cuántas chicas hay en la clase?
b) Si el número de chicas de 1º B supera en cuatro al de chicos, ¿cuántos chicos
hay?
Answer:
I will answer in English.
In each group, A and B, we have 24 students.
a) The number of girls in A is twice the number of boys in A.
Then, if G is the number of girls and B the number of boys.
G + B = 24
G = 2B
Now we can replace the second equation into the first one:
2B + B = 24
3B = 24
B = 24/3 = 8
G = 24 - 8 = 16
We have 16 girls in class A.
b) In B we have 4 more girls than boys, then:
G = B + 4
G + B = 24
we can replace the first equation into the second one:
B + (B + 4) = 24
2*B = 24 - 4 = 20
B= 20/2 = 10
We have 10 boys in class B:
Which graph represents y<-3x?
Step-by-step explanation:
Desmos Graphing Calculator
is the ordered pair (-4,3) a solution of the equation y=5x + 21
Answer:
Step-by-step explanation:
If you substitute x = -4 in the equation, you should get the y value as 3
y = 5x + 21
= 5* -4 + 21
= -20 + 21
y = -1 ≠ 3
So, (-4, 3) is not a solution
Dos motos, A y B, toman la salida en una carrera de 90 km. La moto A realiza el recorrido con una velocidad media inferior en 20 km/h a la de la moto B, con lo que llega a la meta 3 minutos después que B. Calcula la velocidad de cada moto.
Answer:
motorcycle A: 180 km/h
motorcycle B: 200 km/h
Step-by-step explanation:
To solve this question we need to write a system of equations for A and B, using the equation:
distance = speed * time
The speed of A is 20 less than the speed of B, so:
speedA = speedB - 20
And the time A traveled is 3 minutes (0.05 hours) more than B's time, so:
timeA = timeB + 0.05
Then, using the distance equation, we have that:
distanceB = speedB * timeB
90 = speedB * timeB
distanceA = speedA * timeA
90 = (speedB - 20) * (timeB + 0.05)
90 = speedB * timeB + 0.05 * speedB - 20*timeB - 1
90 = 90 + 0.05 * speedB - 20*timeB - 1
20*timeB = 0.05 * speedB - 1
timeB = (speedB - 20)/400
using this timeB in the distance equation, we have:
90 = speedB * (speedB - 20)/400
90 * 400 = speedB^2 - 20*speedB
speedB^2 - 20*speedB - 36000 = 0
Solving this quadratic equation, we have speedB = 200 km/h
And the speedA is:
speedA = speedB - 20 = 200 - 20 = 180 km/h
Length of DE is ___
units.
Length of DB is ___
units.
Measure of angle FED is ___
degrees.
Answer:
Length of DE = 7.5 units
Length of DB = 9.2 units
Measure of ∠FED = 82°
Step-by-step explanation:
In ΔABC,
AD ≅ BD and CE ≅ BE [Given]
By the theorem of mid-segments,
DE = [tex]\frac{1}{2}(AC)[/tex]
= [tex]\frac{1}{2}(15)[/tex]
DE = 7.5 units
Since AD ≅ FE ≅ 9.2 [By midpoint theorem in ΔACB]
Therefore, length of DB = 9.2 units
[Although it's not given in the question, but we assume FE║AB]
Since FE║AB and DE is a transverse,
Therefore, m(∠FED) ≅ m(∠BDE) ≅ 82° [Interior alternate angles]
A set of data includes 107 data points ranging from 0 – 300. If the data is split into classes with a range of 50 (1 – 50, 51 – 100, etc), and there are no values that fall in the class 201 – 350, what can you say about the data? a.All the data lies below 200. b.The median could be in the range 201 - 350. c.The relative frequency of the class 201 - 350 is 0. d.The mean of the data will not be between 201 - 350.
Answer:
D
Step-by-step explanation:
The mean is the average summing all values together and dividing by the number of values been investigated.
Hence since no values exist between 201-350 that means the mean can not be there.
Answer:
The relative frequency of the class 201 - 350 is 0.
Step-by-step explanation:
How many complex numbers have modulus of 5?
9514 1404 393
Answer:
an infinite number
Step-by-step explanation:
In the complex plane, all of the numbers with modulus 5 form a circle of radius 5 around the origin. There are an infinite number of points on that circle.
An infinite number of complex numbers have a modulus of 5.
If (x - 3) represents the side of a cube, what is the
polynomial that represents its volume?
Answer:
x³ - 9x² + 27x - 27
Step-by-step explanation:
The volume (V) of a cube is calculated as
V = s³ ( s is the measure of the side ) , thus
V = (x - 3)³
= (x - 3)(x - 3)(x - 3) ← expand the second/ third factors using FOIL
= (x - 3)(x² - 6x + 9) ← distribute
= x³ - 6x² + 9x - 3x² + 18x - 27 ← collect like terms
= x³ - 9x² + 27x - 27
Debra wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 15 inches by 7 inches by 9 inches. She has 1 square yard of fabric. Can she completely cover the footrest? Explain.
Answer:
Yes, she can.
Step-by-step explanation:
We have to find the surface area of the footrest and see if it greater than or less than 1 square yard.
The surface area of a rectangular prism is given as:
A=2(wl+hl+hw)
where w = width, l = length, h = height
The footrest is 15 inches by 7 inches by 9 inches. Its surface area is:
A = 2[(7 * 15) + (9 * 15) + (9 * 7)]
A = 2[105 + 135 + 63]
A = 2 * 303 = 606 square inches
1 square inch = 0.000771605 square yards
=> 606 square inches = 606 * 0.000771605 = 0.468 square yards
Since the surface area of the prism is less than 1 square yard, she can completely cover the footrest with the fabric.
Which number is an integer?
-3/4 1/5 2 42/3
The Answer:
2 is an integer.
Answer:
c
Step-by-step explanation:
edgeinuity
Sam and Bruno were computing how many kilometers they rode in the 3 bike trips they took last month. In order, they rode 45.7, 40.9, and 38 miles. Their solutions are shown. Sam’s Solution Bruno’s Solution If one kilometer equals 0.621 miles, which is the best solution to find the total number of kilometers they rode? Why is it correct?
Answer:
Bruno will do 45.7
Step-by-step explanation:
1- gather all info
2-subtract
3- YOURE answer
2.
85, 78, 82, 76, 89, 77, 78, 42, 83, 84, 87, 85, 78
What effect does the outlier have on the mode of this data?
1. The mode increases.
2. The mode decreases.
3. The mode cannot be calculated.
4. The mode remains the same.
Answer:
the mode remains the same
Step-by-step explanation:
42 is outlier.
mod is the most repetitive number of a number string, and outlier does not change it.
the mode remains the same.
Simplify the following expressions by using distributive property. 3x^2(4x-3)
Answer:
12x^3-9x^2
Step-by-step explanation:
[tex]3x^2(4x-3)= \\\\3x^2(4x)+3x^2(-3)= \\\\12x^3-9x^2[/tex]
Hope this helps!
find the y-intercept for parabola defined by this equation: y=-4x^2-x+3
Answer:
(0,3)
Step-by-step explanation:
An easy way to determine the y intercept of a function is to graph it, and to see where the function passes through the y axis. As you can see below, the y intercept of this graph is at (0,3). Hope this helps!
Answer:
Y intercept = (0,3)
Step-by-step explanation:
When looking at a equation like this the y intercept would always the the number without a variable beside it.
-x would be the slope of the function
So 3 is your y intercept
Hope this helps!
Just the top half is what I need help with. I will give the the big
Answer:
Step-by-step explanation:
5.volume=8×7×6=336 mi³
6.r=16/2=8 yd
volume=4/3×π×8³=2048/3 π yd³
≈2144.7 yd³
7.r=2.5/2=1.25 in
v=πr²h=π×1.25²×5
volume of 150 cups=7.8125 π×150=1171.875 π in³≈3681.6 in³
8. statement not visible.
Help PLZZZ
Describe the change in the graph of the parabola f(x) when it transforms into g(x) = two thirdsf(x).
A The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
BThe parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
CThe parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
D The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Answer:
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
Answer:
It's B.
Step-by-step explanation:
I took the test.
What is the value of x ?
Answer:
x=22
Step-by-step explanation:
set all of your values equal to 360 (bc thats the value of the degrees in a circle) and then solve for x!
75 + 92 + ( x+57 ) + ( x+92) = 360
( x+57 ) + ( x+92 ) = 201
2 x = 44
x = 22
How do I solve this?
A=bh/2
A=2/3ft*3/5ft/2
A=2/3×5/5*3/5×3/3/2
A=10/15*9/15/2
A=90÷15/2
A=6ft^2
Answer:
The area of triangle is 1/5 feet².
Step-by-step explanation:
You have to use area of triangle formula, A = 1/2×height×base. Then substitute the following values into the formula :
[tex]area = \frac{1}{2} \times height \times base[/tex]
Let height = 3/5,
Let base = 2/3,
[tex]area = \frac{1}{2} \times \frac{3}{5} \times \frac{2}{3} [/tex]
[tex]area = \frac{1}{2} \times \frac{1}{5} \times \frac{2}{1} [/tex]
[tex]area = \frac{1}{2} \times \frac{2}{5} [/tex]
[tex]area = \frac{1}{5} {feet}^{2} [/tex]
solve the equation for x -x*2-10x+24=0
Answer:
x=-12 x =2
Step-by-step explanation:
-x^2-10x+24=0
Divide by -1
x^2 +10x -24 = 0
Factor
What 2 terms multiply to -24 and add to 10
12 * -2 = -24
12 -2 = 10
(x+12) ( x-2) = 0
Using the zero product property
x+12 =0 x-2 =0
x=-12 x =2
The ratio of the same side interior angles of two parallel lines is 1:14. Find the measures of all eight angles formed by the parallel lines and transversal. Sorry! Would appreciate if you give the answer by Tuesday! Thanks
Answer:
At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.
At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.
Step-by-step explanation:
Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.
We know that the sum of interior angles equals 180°.
So, a + b = 180°
a + 14a = 180°
15a = 180°
a = 180/15
a = 12°
At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°
The angle vertically opposite to a is d = a = 12°
The angle vertically opposite to a is b = e = 168°
At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°
the angle vertically opposite to angle b is g = b = 168°
the angle vertically opposite to f is h = 12°
Given that the same-side interior angles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:
m<1 = 12°
m<2 = 168°
m<3 = 168°
m<4 = 12°
m<5 = 12°
m<6 = 168°
m<7 = 168°
m<8 = 12°
Applying the knowledge of ratio, transversal and parallel lines, we can determine the measures of all 8 angles that are formed when a transversal intersects two parallel lines as shown in the image attached below.
Let < 1 and < 6 be the two same-side interior angles whose measures are in the ratio, 1:14.
Thus:
m<1 : m<6 = 1 : 14Recall:
Same-side interior angles are always supplementary. That is,
m<1 + m<6 = 180 degrees.
Let's apply ratio to find the measure of <1 and <6.
m<1 = ratio of <1 / sum of ratio x 180[tex]m \angle 1 = \frac{1}{1 + 14} \times 180\\\\m \angle 1 = \frac{1}{15} \times 180\\\\m \angle 1 = 12^{\circ}[/tex]
m<6 = ratio of <6 / sum of ratio x 180[tex]m \angle 6 = \frac{14}{1 + 14} \times 180\\\\m \angle 6 = \frac{14}{15} \times 180\\\\m \angle 6 = 168^{\circ}[/tex]
Since we know the measure of <1 and <6, we can find the measure of others as follows:
m<2 = m<6 = 168° (corresponding angles are congruent)m<3 = m<6 = 168° (alternate interior angles are congruent)m<4 = m<1 = 12° (vertical angles are congruent)m<5 = m<1 = 12° (corresponding angles are congruent)m<7 = m<6 = 168° (vertical angles are congruent)m<8 = m<4 = 12° (corresponding angles are congruent)In conclusion, given that the same-side interior angles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:
m<1 = 12°
m<2 = 168°
m<3 = 168°
m<4 = 12°
m<5 = 12°
m<6 = 168°
m<7 = 168°
m<8 = 12°
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What is the length of AC? And Length of AB?
Answer:
The length of AC is 5 units. The length of AB is 3 units.
Step-by-step explanation:
which phrase represents the algebraic expression 3p + 6
Answer:9p
Step-by-step explanation:
If the measure of angle 1 is (3x-4)º and the measure of angle 2 is (4x+10), what is the measure of angle 2 in degrees?
HELP !!!!!!!!!!!!!!!!!!!! Plz !!!!!!
Answer:
Angle 2 measures 58°
Step-by-step explanation:
Sum of all three angles formed = 180
Because the sum of angles on a straight line is always 180
Angle 1 =3x-4
Angle 2 = 4x+10
Angle 3= 90° (given)
So,
90+3x-4+4x+10=180
(4x+3x)+(90+10-4)= 180
7x+96=180
Bring 96 to the other side, making it negative,
7x = 180-96 = 84
x = 12
Therefore angle 2
= 4x+10
= (4)(12)+10
=48+10
=58°
