Answer:
1. 20 tins of milk
2. Weight of the Carton = 8,4kg ot 8400g
Step-by-step explanation:
Given
Volume of a Tin = 77cm³
Weight of a tin = 5000g
Volume of Empty Carton = 1540cm³
Weight of Empty Carton = 5000g
Calculating the number of tins of milk
To do this, we have to make use of the given volumes;
And this is done as follows;
[tex]Number = \frac{Volume\ of\ Empty\ Carton}{Volume\ of\ a\ Tin}[/tex]
Substitute 77cm³ for Volume of a Tin and 1540cm³ for Volume of an Empty Carton
[tex]Number = \frac{1540cm^3}{77cm^3}[/tex]
[tex]Number = 20[/tex]
Hence, 20 tins of milk will filled the empty carton
Calculating the weight of the Carton after filled with tins of milk
This is calculated as thus;
Total Weight = Weight of Empty Carton + Weight of Tins of Milk
Substitute 5000g for Weight of Empty Carton
Total Weight = 5000g + Weight of Tins of Milk
_________________________________________
Calculating Weight of Tins of Milk
Since 20 tins of milk will fill the empty carton, the
Weight of Tins of Milk = 20 * Weight of 1 Tin of Milk
Weight of Tins of Milk = 20 * 170g
Weight of Tins of Milk = 3400g
_________________________________________
Substitute 3400g for Weight of Tins of Milk
[tex]Total\ Weight = 5000g + 3400g[/tex]
[tex]Total\ Weight = 8400g[/tex]
In Kilograms:
[tex]Total\ Weight = 8.4kg[/tex]
please tell me the method and answer of 2nd question
Answer:
see explanation
Step-by-step explanation:
In a trapezium the lower base angle is supplementary to the upper bas angle on the same side, thus
4x + 91 - 9x + 59 = 180, that is
- 5x + 150 = 180 ( subtract 150 from both sides )
- 5x = 30 ( divide both sides by - 5 )
x = - 6
Thus
∠ N = - 9x + 59 = - 9(- 6) + 59 = 54 + 59 = 113°
∠ K = 4x + 91 = 4(- 6) + 91 = - 24 + 91 = 67°
PLs help ASAP will make you brainist
Answer:
c.18
Step-by-step explanation:
32/24=1.33333333333
40/30=1.33333333333
24/1.33333333333=18
Side ST correlates to side BC. Let's use these two sides to find the scale factor between the two triangles
[tex]\text{Scale Factor}=\dfrac{30}{40}=\dfrac{3}{4}[/tex]
Triangle ABC has side lengths are the 3/4 smaller than that of RTS. The value of x is the length of side AC, which correlates with side RS
Multiply 24 by 3/4 to find the value of x
[tex]x=\dfrac{3}{4}\times24=18[/tex]
This is answer choice C. Let me know if you need any clarifications, thanks!
How many real solutions In this problem
Answer:
D
Step-by-step explanation:
Given
y = x² + 1
y = x
Equating gives
x² + 1 = x ( subtract x from both sides )
x² - x + 1 = 0
Consider the discriminant Δ = b² - 4ac
with a = 1, b = - 1 and c = 1
b² - 4ac = (- 1)² - (4 × 1 × 1) = 1 - 4 = - 3
Since b² - 4ac < 0 then there are no real solutions
Drag a statement or reason to each box to complete this proof.
If -5(x + 8) = -25, then x =
-3
A circle with center A and radius three inches is tangent at C to a circle with center B, as shown. If point B is on the small circle, what is the area of the shaded region? Express your answer in terms of \pi.
Answer:
27π Sq in.
Step-by-step explanation:
Circle A is equal to 9π sq inches. (Radius squared times Pi), Segment BC is a radii of Circle B and the diameter of Circle A. Meaning Circle B's radius is 6 inches. The area of circle B would be 36π sq inches. Now we subtract Circle A's area from Circle B's area(36π sq in. - 9π sq in.), the area of the shaded region is 27π sq in.
A lake has a small patch of lily pads and every day the patch grows to double its size. It takes 32 days for the patch to cover the lake – how long would it take the patch to cover half the lake?
Answer:
It took 31 days for the patch to cover half the lake
Step-by-step explanation:
The patch grows to double its size everyday
the patch completely covers the lake in 32 days
Since the patch doubles itself everyday, this means that the previous day before the 32nd day, the lake was just half covered.
Therefore, the the patch covered half the lake on the 31st day, i.e it took 31 days for the patch to cover half the lake
What is the value of discontinuity of x^2+8x+4/x^2-x-6? Choices:
Answer:
-2
Step-by-step explanation:
Hello,
First of all, let's check the denominator.
[tex]x^2-x-6 \ \ \text{ *** How to factorise it ...? ***}\\\\\text{*** The product of the roots is -6=-2*3 and their sum is 1 ***}\\\\x^2-x-6=x^2-3x+2x-6=x(x-3)+2(x-3)=(x+2)(x-3)[/tex]
Now, let's see the numerator.
[tex]x^2+8x+4 \ \text{ *** -2 is not a zero as ***}\\\\(-2)^2+8*(-2)+4=4-16+8=-4\\\\\text{*** 3 is not a zero as ***}\\\\3^2+8*3+4=9+24+4=37\\[/tex]
So we cannot factorise the numerator with (x+2) or (x-3)
Then, -2 and 3 are the the discontinuities of the expression.
There is only -2 in the list, this is the correct answer.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
In a local town, 54,000 families have incomes less than $25,000 per year. This number of families is 60% of the families that had this income level 12 years ago. What was the number of families who had incomes less than 25,000 per year 12 years ago
Answer: 90,000
Step-by-step explanation:
From the question, we are informed that in a local town, 54,000 families have incomes less than $25,000 per year. We are further told that this number of families is 60% of the families that had this income level 12 years ago.
To calculate the number of families who had incomes less than 25,000 per year 12 years ago goes thus:
Let the the number of families who had incomes less than 25,000 per year 12 years ago be represented by x.
Since we are told that this number of families is 60% of the families that had this income level 12 years ago. This means that:
60% of x = 54,000
60/100 × x = 54,000
0.6 × x = 54,000
0.6x = 54,000
Divide by 0.6
0.6x/0.6 = 54000/0.6
x = 90,000
The number of families who had incomes less than 25,000 per year 12 years ago was 90,000.
Natasha and her two dogs were walking on a perfectly straight road when her two dogs ran away from her in opposite directions. Her beagle is now \dfrac{25}{4} 4 25 start fraction, 25, divided by, 4, end fraction meters directly to her right, and her labrador is \dfrac{51}{20} 20 51 start fraction, 51, divided by, 20, end fraction meters directly to her left. Which of the following expressions represents how far apart the two dogs are?
Answer:
[tex]\dfrac{74}{20}=3.7 meters[/tex]
Step-by-step explanation:
Hello!
1) Since no other data has been given. Suppose Natasha is in the center and the beagle is to the right.
[tex]\dfrac{25}{4} \:meters[/tex]
2) The labrador is [tex]\dfrac{51}{20}\: to\: the\: left.[/tex]
[tex]\dfrac{25}{4} -\dfrac{51}{20} =\dfrac{(5*25)-51}{20} \\\dfrac{(125-51}{20} =\dfrac{74}{20}[/tex]
Answer:
The answer is B :D hope this helps
Step-by-step explanation:
2.) Evaluate 6a² if a = 4
Answer:
96
Step-by-step explanation:
We simply need to plug in a = 4 so 6a² = 6 * 4² = 6 * 16 = 96.
7 3/8 + (-4 1/2) ÷ (-5 2/3) Please Explain
Answer:
7 3/8 + (-4 1/2) ÷ (-5 2/3) = 8 23/136
Step-by-step explanation:
1) First I turned all the mix numbers into improper fractions:
7 3/8 ----> ( 7(8)+3/8) = 59/8, 4 1/2 ----> (4(2)+1/2) = 9/2, 5 2/3 ----> (5(3)+2/3) = 17/3
So now it should look like this: 59/8 + (-9/2)÷(-17/3)
2) Now our goal is to divide both of the improper fractions (-9/2)÷(-17/3),
- We first apply our fraction rule: -a/-b = a/b (when we have two negatives they cancel out each other and make a positive)
Our Case, From this:-9/2 ÷ -17/3 = To This: 9/2 ÷ 17/3
3) Now we can divide the fractions using this rule: a/b ÷ c/d = a times d / b times
Our Case, From This: 9/2 ÷ 17/3 To This: 9(3)/2(17) Which Gives Us: 27/34
(9 x 3 = 27, 2 x 17= 34)
So now it looks like this: 59/8 +27/34
4) Our look goal is to have the same denominator (which is the bottom part of the fraction) which are 8 and 34
To find it we find the LCM or Least Common Multiple of 8 and 34
(The LCM of a, b is the smallest positive number that is divisible by both a and b) which in this case a and b are 8 and 34
LCM is 136
5) We adjust our two fractions based on the LCM,
(Multiply each numerator ( top part of the fraction) by the same amount of needed to multiply its corresponding denominator to turn it to the LCM 136.
From This: 59/8 and 27/34 To This: 1003/136 and 108/36 ( 59(17)/8 (17) = 1003/136, 27(4)/34(4) = 108/306
6) Finally we can add the numerator (1003 and 108) together: 1003+108= 1111 and now we are left with 1111/136
Then we turn our improper fraction back into a mix number: 1111/138= 8 23/136
Answer:
[tex]\frac{1111}{136} = 8 \frac{23}{136}[/tex]
Step-by-step explanation:
We want to simplify:
[tex]7 \frac{3}{8} + \frac{ -4 \frac{1}{2} }{ -5 \frac{2}{3} }[/tex]
First, convert all the fractions to improper fractions:
[tex]\frac{59}{8} + \frac{ - \frac{9}{2} }{ - \frac{17}{3} } \\\\= \frac{59}{8} + \frac{27}{34}[/tex]
Find the LCM of the denominators:
[tex]\frac{(17 * 59) + (4 * 27)}{136} \\\\ = \frac{1003 + 108}{136}\\ \\= \frac{1111}{136} \\\\= 8 \frac{23}{136}[/tex]
In a survey men in a certain country (ages 20-29), the mean height was 62.8 inches with a standard deviation of 2.8 inches, what height represents the 99th percentile?
Answer:
the height that represents the 99th percentile is 69.324 inches
Step-by-step explanation:
Given that :
the mean height = 62.8 inches
standard deviation = 2.8 inches
For 99th percentile;
Let X be the random variable;
SO, P(Z≤ z) = 0.99
From the standard normal z tables
P(Z )= 2.33
The standard z score formula is :
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
[tex]2.33 = \dfrac{X- 62.8}{2.8}[/tex]
2.33 × 2.8 = X - 62.8
6.524 = X - 62.8
6.524 +62.8 = X
69.324 = X
X = 69.324
Therefore; the height that represents the 99th percentile is 69.324 inches
EXPLANATION NEEDED:
In right triangle ABC, ∠ B is a right angle and sin ∠ C = x. cos ∠ A =
a. √x² - 1
b. √1 - x²
c. x
d. √x² + 1
e. x²
Answer:
C. xStep-by-step explanation:
AC denotes the length of the hypotenuse and AB and BC denote the lengths of the other two sides, so:
[tex]\cos(\angle A)=\dfrac{AB}{AC}=\sin(\angle C)=x[/tex]
a
simplified form of -3 + 2(x - 1)?
8. Which expression
a. -X + 1
b. 2x-5
c. 2x - 4
d. -X-1
Answer:
2x -5
Step-by-step explanation:
-3 + 2(x - 1)
Distribute
-3 +2x -2
Combine like terms
2x -5
Answer:
5x -2
Step-by-step explanation:
Find the mean and standard deviation. Show all work. 1. X 0 1 2 3 4 P(x) .07 .38 .22 .13
Answer:
Mean = 2.14
Standard deviation = 2.40
Step-by-step explanation:
The calculation of mean and standard deviation is shown below:-
[tex]X = .07\times0 + 0.20\times 1 + 0.38\times 2 + 0.22\times 3 + 0.13\times 4\\\\ = 0 + 0.2 + 0.76 + 0.66 + 0.52[/tex]
= 2.14
So, the mean is 2.14
Now, For computing the standard deviation first we need to find out the variance which is shown below:-
Variance is
[tex]Var(X) = P(X^2) - [P(X)]^2\\\\ P(X^2) = .07\times (0^2) + .20\times (0^1) + .38\times (0^2) + .22\times (0^3) +0.13\times (0^4)[/tex]
After solving the above equation we will get
= 5.78
Now, the standard deviation is [tex]= \sqrt{Variance}[/tex]
[tex]= \sqrt{5.78}[/tex]
= 2.404163056
or
= 2.40
Complete the square to rewrite y = x2 + 8x+ 3 in vertex form, and then identify
the minimum y-value of the function.
Please answer ASAP!!!
====================================================
Work Shown:
y = x^2 + 8x + 3 is the same as y = 1x^2 + 8x + 3
It is in the form y = ax^2 + bx + c
a = 1
b = 8
c = 3
Plug the values of a and b into the formula below to get the x coordinate of the vertex (h,k)
h = -b/(2a)
h = -8/(2*1)
h = -8/2
h = -4
Plug this into the original equation to get its paired y value. This will get us the value of k
y = x^2 + 8x + 3
y = (-4)^2 + 8(-4) + 3
y = 16 - 32 + 3
y = -13
This is the smallest y output possible. Therefore it is the minimum. The minimum occurs at the vertex (h,k) = (-4, -13)
We know we are dealing with a minimum because a = 1 is positive forming a parabola that opens upward. If a < 0, then the parabola would open downward to yield a maximum.
Find the center and radius of x^2 – 18x + y^2 -10y = -6. part two write x2 – 18x + y2 -10y = -6 in standard form
Answer:
see explanation
Step-by-step explanation:
I will begin with part two, first.
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius.
Given
x² - 18x + y² - 10y = - 6
Using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 9)x + 81 + y² + 2(- 5)y + 25 = - 6 + 81 + 25, that is
(x - 9)² + (y - 5)² = 100 ← in standard form
with centre = (9, 5 ) and r = [tex]\sqrt{100}[/tex] = 10
Find the volume in cubic meters, of the 3-Dimensional composite
figure.
8m
5m
Answer:
890 m^3 to the nearest whole number.
Step-by-step explanation:
Volume = volume of the cylinder + volume of the hemisphere:
= π r^2 h + 1/2 * 4/3 π r^3
= π*5^2 * 8 + 1/2 * 4/3 π 5^3
= 890.12
Please answer it now in two minutes
Answer:
y = 4
Step-by-step explanation:
Using the tangent ratio in the right triangle and the exact value
tan30° = [tex]\frac{1}{\sqrt{3} }[/tex] , then
tan30° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{4\sqrt{3} }[/tex] = [tex]\frac{1}{\sqrt{3} }[/tex] ( cross- multiply )
y × [tex]\sqrt{3}[/tex] = 4[tex]\sqrt{3}[/tex] ( divide both sides by [tex]\sqrt{3}[/tex] )
y = 4
Answer:
y=4
Step-by-step explanation:
If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.
So, by the law of sines we can say that:
[tex]\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}[/tex]
Solving for y, we get:
[tex]sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4[/tex]
In a local ice sculpture contest, one group sculpted a block into a rectangular based pyramid. The dimensions of the base were 3 m by 5 m, and the pyramid was 3.6 m high. Calculate the amount of ice needed for this sculpture.
Answer:
18m square
Step-by-step explanation:
Formula for rectangular- based pyramid is L x W x H divided by 3
= 3 x 5 x 3.6 divided by 3 = 18
So you would need 18 m square for the sculpture
S and T are two-digit positive integers that have the same digits but in reverse order. If the positive difference between S and T is less than 40, what is the greatest possible value of S minus T
Answer :Answer: Did you get helped on this one?
Step-by-step explanation: okay yup yup have a good day OKAY
Step-by-step explanation: HAVE A GOOD ONE OKAY
from the figure below identify a)Obtuse vertically opposite angles b) A pair of adjacent complementary angles c) a pair of equal supplementary angles d) a pair of unequal supplementary angles e) a pair of adjacent angles that don’t form a linear pair
Answer:
a) BOC and AOD
b) BOA and AOE
c) BOE and EOD
d) BOA and AOD
e) AOE and EOD
Step-by-step explanation:
An obtuse angle is an angle that has more than 90° and vertically opposite angles are angle formed by two lines crossed. So, Obtuse vertically opposite angles are BOC and AOD
Adjacent angles are angles in which one angle is beside the other and complementary angles are angles whose sum is equal to 90°, so, a pair of adjacent complementary angles are BOA and AOE.
Supplementary angles are angles whose sum is equal to 180°, so BOE and EOD are equal suplementary angles and BOA and AOD are unequal supplementary angles
Finally, AOE and EOD are adjacent angles that don’t form a linear pair.
f(x)=x^2. What is g(x)?
Answer:
A
Step-by-step explanation:
With this one, you can just plug in 3 into each of the equations until the answer is 1.
When u plug 3 into x for solution A.
(1/3)×3=1
1^2=1
Answer:
[tex]\boxed{ \mathrm{A} }[/tex]
Step-by-step explanation:
The point is given (3, 1)
x = 3
y = 1
y = (1/3x)²
Plug x as 3 and y as 1.
The equation should be equal.
1 = (1/3(3))²
1 = 1²
1 = 1 True
A. 60
B. 15
C. 120
D. 6
Answer:
C. 120
Step-by-step explanation:
The figure shows that angles BEC and KEC are congruent. Their measures are equal.
m<KEC = m<BEC
10x = 6x + 24
4x = 24
x = 6
m<BEK = 2m<KEC
m<BEK = 2 * 10x
m<BEK = 2 * (10)(6)
m<BEK = 2 * 60
m<BEK = 120
What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞) SORRY THIS IS THE FULL QUESTION
Answer:
[15, ∞).
Step-by-step explanation:
–3(6 – 2x) ≥ 4x + 12
-18 + 6x ≥ 4x + 12
6x - 4x ≥ 12 + 18
2x ≥ 30
x ≥ 15
This means that the minimum of x is 15, and the most is infinity, which is the same thing as [15, ∞).
Hope this helps!
ese
i). nx n2 =343 (2mks)
I
Answer:
Are you asking what the value of x is if [tex]n^{x} * n^2 = 343[/tex] ?
Step-by-step explanation:
What is the slope of the line shown below? (-2,3) (-4,-9)
Answer:
6Step-by-step explanation:
Let the points be A and B
A ( - 2 , 3 ) -------> ( x1 , x2 )
B ( -4 , -9 ) -------> ( x2 , y2 )
Now, finding the slope:
[tex]slope \: (m) = \frac{y2 - y1}{x2 - x1} [/tex]
Plug the values
[tex] = \frac{ - 9 - 3}{ - 4 - ( - 2)} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 4 - ( - 2)} [/tex]
When there is a (-) in front of an expression in parentheses , change the sign of each term in expression
[tex] = \frac{ - 12}{ - 4 + 2} [/tex]
Calculate
[tex] = \frac{ - 12}{ - 2} [/tex]
Reduce the fraction with -2
[tex] = 6[/tex]
Hope this helps..
Best regards!!
I promise I will mark as brainiest
There are 18 rectangles inside the playing field. And if you include the fence around the field, that makes 19.
n the diagram below, points $A,$ $E,$ and $F$ lie on the same line. If $ABCDE$ is a regular pentagon, and $\angle EFD=90^\circ$, then how many degrees are in the measure of $\angle FDE$?
[asy]
size(5.5cm);
pair cis(real magni, real argu) { return (magni*cos(argu*pi/180),magni*sin(argu*pi/180)); }
pair a=cis(1,144); pair b=cis(1,72); pair c=cis(1,0); pair d=cis(1,288); pair e=cis(1,216);
pair f=e-(0,2*sin(pi/5)*sin(pi/10));
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f);
label("$A$",a,WNW);
label("$B$",b,ENE);
label("$C$",c,E);
label("$D$",d,ESE);
label("$E$",e,W);
label("$F$",f,WSW);
draw(d--f--a--b--c--d--e);
draw(f+(0,0.1)--f+(0.1,0.1)--f+(0.1,0));
[/asy]
Answer:
18
Step-by-step explanation:
Each interior angle of a regular pentagon is 108 degrees. So Angle AED is 108 degrees. Since Angle AEF is a straight line (180 degrees), Angle FED is 72. This is because 180-108 = 72. Now, since a triangle has a total of 180 degrees, we add 72 and 90, because those are the 2 degrees we have calculated. This gives us a total of 162. Now, we subtract 162 from 180 to find out the degree of Angle FDE. This is 18. So our final answer is 18.
Sidenote: I hope this answer helps!
The properties of a pentagon and the given right triangle formed by
segments EF and FD give the measure of ∠FDE.
Response:
∠FDE = 18°Which properties of a pentagon can be used to find ∠FDE?The given parameters are;
A, E, F are points on the same line.
ABCDE is a regular pentagon
∠EFD = 90°
Required:
The measure of ∠FDE
Solution:
The points A and E are adjacent points in the pentagon, ABCDE
Therefore;
line AEF is an extension of line side AE to F
Which gives;
∠DEF is an exterior angle of the regular pentagon = [tex]\frac{360 ^{\circ}}{5}[/tex] = 72°∠EFD = 90°, therefore, ΔEFD is a right triangle, from which we have;
The sum of the acute angles of a right triangle = 90°
Therefore;
∠DEF + ∠FDE = 90°
Which gives;
72° + ∠FDE = 90°
∠FDE = 90° - 72° = 18°
∠FDE = 18°
Learn more about the properties of a pentagon here:
https://brainly.com/question/15392368
Solve the inequality 47.75 + x Less-than-or-equal-to 50 to determine how much more weight can be added to Li’s suitcase without going over the 50-pound limit. What is the solution set?
x Less-than-or-equal-to 2.25
x Less-than-or-equal-to 2.75
x Greater-than-or-equal-to 2.25
x Greater-than-or-equal-to 2.75
Answer: x Less-than-or-equal-to 2.25
Step-by-step explanation:
The given inequality: 47.75 + x Less-than-or-equal-to 50.
To determine: How much more weight can be added to Li’s suitcase without going over the 50-pound limit.
i.e. inequality for x.
[tex]47.75+x\leq50[/tex]
Subtract 47.75 from both the sides, we get
[tex]x\leq50-47.75\\\\\Rightarrow\ x\leq2.25[/tex]
So, the solution set is "x Less-than-or-equal-to 2.25"
Hence, the correct answer is "x Less-than-or-equal-to 2.25."
Answer
A x <_ 2.25
Step-by-step explanation: