Question:
A rectangular prism has a length of 4 1/2 millimeters, a width of 4 1/2 millimeters, and a height of 6 millimeters.
Sally has a storage container for the prism that has a volume of 143 cubic millimeters.
What is the difference between the volume of the prism and the volume of the storage container?
Answer:
The difference between the volume of the prism and the volume of the storage container is 21.5 cubic millimeter
Solution:
Volume of rectangular prism is given as:
[tex]volume = length \times width \times height[/tex]
From given,
[tex]length = 4\frac{1}{2} = \frac{9}{2}\ mm\\\\width = 4\frac{1}{2} = \frac{9}{2}\ mm\\\\height = 6\ mm[/tex]
Therefore,
[tex]volume = \frac{9}{2} \times \frac{9}{2} \times 6 = 121.5\ mm^3[/tex]
Sally has a storage container for the prism that has a volume of 143 cubic millimeters
What is the difference between the volume of the prism and the volume of the storage container
Difference = 143 - 121.5 = 21.5
Thus difference between the volume of the prism and the volume of the storage container is 21.5 cubic millimeter
What’s 5x divided by 6=20
Answer:
24
Step-by-step explanation:
5x/6=20
Multiple 20 by 6 then you get 120.
Then divide 120 by 5 which is 24.
Answer:
x = 24
Step-by-step explanation:
Simplify both sides of the equation, then isolate the variable.
What is the difference of the two polynomials?
(92+8)–(22+3)
Answer:
75
Step-by-step explanation:
(92+8)-(22+3)
Add the terms inside of the parentheses because of PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)
(100)-(25)
Then subtract 25 from 100
75
Maria brought 17 packs of cola to a party , and each pack had 6 cans . Heather brought 9 cans of juice . How many cans did they bring in all ?
Answer:
Step-by-step explanation:
Maria:
No. of cans in a pack = 6
No.of cans in 17 pack = 6 * 17 = 102 cans
No. of cans bought by Heather = 9 cans
Total cans = 102 + 9 = 111 cans
What is the length and width of a rectangle given by the trinomial r squared - 6r- 55? Use factoring
The length of the rectangle is 11 units
The width of the rectangle is 5 units.
Explanation:
The equation of the trinomial is [tex]r^{2}-6 r-55[/tex]
We need to find the length and the width of the rectangle.
The length and width of the rectangle can be determined by factoring the trinomial [tex]r^{2}-6 r-55=0[/tex]
Factoring using the quadratic formula, we have,
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
where [tex]a=1, b=-6[/tex] and [tex]c=-55[/tex]
Substituting these in the above formula, we have,
[tex]r=\frac{-(-6) \pm \sqrt{(-6)^{2}-4 \cdot 1(-55)}}{2 \cdot 1}[/tex]
[tex]r=\frac{6\pm \sqrt{36+220}}{2}[/tex]
[tex]r=\frac{6\pm \sqrt{256}}{2}[/tex]
[tex]r=\frac{6\pm 16}{2}[/tex]
Hence, the two roots of the trinomial are
[tex]r=\frac{6+ 16}{2}[/tex] and [tex]r=\frac{6- 16}{2}[/tex]
Solving [tex]r=\frac{6+ 16}{2}[/tex] , we get,
[tex]r=\frac{22}{2}[/tex]
[tex]r=11[/tex]
Solving [tex]r=\frac{6- 16}{2}[/tex] , we get,
[tex]r=\frac{-10}{2}[/tex]
[tex]r=-5[/tex]
Thus, the solutions of the trinomial are 11 and -5
Since, the length of the rectangle is larger than the width, the length of the rectangle is 11 units.
Also, the width of the rectangle cannot be negative.
Thus, ignoring the negative sign, we have, [tex]r=5[/tex]
Hence, the width of the rectangle is 5 units.
Joey has 8 pairs of socks in his drawer. Five of them are white. What percent of colored socks does Joey have.
Which values are solutions to the inequality below? Check all that apply.
Answer:
b,d
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that
x²>18
So, let take the square root of both sides
Then,
√x²>√18
x> ± 4.24
So it is either
x>4.24 or x<-4.24
Either of the two will gives a square higher than 18. You should note that the square of any number is always positive.
The applicable answer are
A. 5
Because
5²=25 which is greater than 18
D. 8
Because
8²= 64 which is greater than 18
F. -18
Because
(-18)²=-18×-18=324 which is greater than 18.
Note : -×-=+
Can this be simplified?
Answer:
0.2+sqrt3/10
Step-by-step explanation:
Ⓗⓘ ⓣⓗⓔⓡⓔ
Well, if I'm reading it correctly, it could be simplified to (1/5)+(sqrt3/10) or 0.2+sqrt3/10.
(っ◔◡◔)っ ♥ Hope this helped, have a great day! ♥
˜”*°•.˜”*°• ~Star •°*”˜.•°*”˜
Plz help ASAP :))))
David is planning a party outside. He googles the weather for that particular day and it says there is a 58% chance of rain. Is it likely to rain or not likely to rain?
A:likely
B:Not likely
Answer:
It would be A:likely
Step-by-step explanation:
let's take rounding decimals for example; when you 5.86 and you were rounding to the nearest tenth it would be 5.9. That is because the 6 is greater than 5, so for the weather the highest the percentage it can be is 100% and 50% is half and since it is more than half then it would be more likely.
Mike and Sam Tun laps. Mike runs a lap in 5 minutes and Sam runs a lap in 6 minutes. If Mike and Sam begin running at the same time, after how many minutes will they cross the starting line at the same time?
Answer: 30 min.
Step-by-step explanation: for this, you have to find the gcf of 5 and 6, which is 30.
Final answer:
Mike and Sam will both cross the starting line together after 30 minutes of running, as 30 minutes is the least common multiple of their individual lap times of 5 and 6 minutes.
Explanation:
To find out how long it will take for Mike and Sam to cross the starting line together again, we need to determine the least common multiple (LCM) of their lap times. Mike runs a lap in 5 minutes and Sam runs a lap in 6 minutes. The LCM of 5 and 6 will give us the first time they both cross the starting line at the same time after they start running.
To calculate the LCM of 5 and 6, we list the multiples of each number until we find a common one:
5, 10, 15, 20, 25, 30, ...
6, 12, 18, 24, 30, ...
The smallest common multiple of 5 and 6 is 30. Therefore, Mike and Sam will both cross the starting line together after 30 minutes of running.
A satellite views the earth at an angle of 20°. What is the arc measure, x, that the satellite can see?
Answer:
The measure of the arc is 160 degrees
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The measure of the external angle is the semi-difference of the arches it covers.
so
[tex]20^o=\frac{1}{2}[(360-x)^o-x^o][/tex]
solve for x
[tex]40^o=360^o-2x[/tex]
[tex]2x=360^o-40^o\\2x=320^o\\x=160^o[/tex]
The arc measure that the satellite can see is 20°.
Explanation:An arc measure is the central angle that corresponds to a given arc on a circle. In this case, the satellite views the earth at an angle of 20°. The arc measure that the satellite can see is also 20°.
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Which of the following is 47 to the
nearest tenth?
OA) 6.9
OB) 8
OC) 68.5
OD 9.2
Its C if you are estimating. But there is no other exact answer.
James drove 6 miles
south and then 3 miles
west. How far is he
from his starting point?
Answer:
9
Step-by-step explanation:
because 3+6=9 so he is 9 miles from his starting point
give the degree of the polynomial
-3w+x^6y^5-2+5y^4w^3x^2
Answer:
Here the degree of the polynomial is 11.
Step-by-step explanation:
To find the degree of the multivariate polynomials, we need to add up the powers of all the variables. So the total degree is given by the sum of all the powers of the highest powers terms.
Now in the given polynomial [tex]-3w+x^6y^5-2+5y^4w^3x^2[/tex]
the term with the highest total powers is [tex]x^6y^5[/tex] and thus the total power is 6+5=11.
And hence the degree of this polynomial is 11.
ERICA WROTE 5 added to y as 5+y and 5 subtracted from y as 5-y.why is the expression correct but the second one incorrect? when is order important in writing an expression?
please help me.....
Answer:
Step-by-step explanation:
Order is impotant since you could easily make a positve number negative and vice versa. You switch the order of 5 subtracted by y to y-5.
Which best describes the following equation of 3 (5x + 8) =4 (6x + 9)
Answer:
x = -4/3
Step-by-step explanation:
Step 1: Distribute
3(5x + 8) = 4(6x + 9)
15x + 24 = 24x + 36
Step 2: Subtract 15x from both sides
15x + 24 - 15x = 24x + 36 - 15x
24 = 9x + 36
Step 3: Subtract 36 from both sides
24 - 36 = 9x + 36 - 36
-12 = 9x
Step 4: Divide both sides by 9
-12 / 9 = 9x / 9
-4/3 = x
Answer: x = -4/3
Oscar bought several bags of lemon drop candy and several bags of jelly beans. The number of bagsof beans was 5 more than the number of bags of lemon drops. Jelly bean bags weigh 8 ounces, and drop bags weigh 16 ounces each. The total weight of all the bags of candy was 400 ounces.
A. Write and solve a system of equations that allows you to solve for how many bags of each candy Oscar bought Show all of your
Answer:
A system of equations that allows you to solve for how many bags of each candy Oscar bought is [tex]16x+8(x+5)=400[/tex] and The number of bags of lemon drops and number of bags of beans are 15 and 20 respectively
Step-by-step explanation:
Let x be the number of bags of lemon drops
We are given that The number of bags of beans was 5 more than the number of bags of lemon drops
So, The number of bags of beans =x+5
Jelly bean bags weigh 8 ounces, and drop bags weigh 16 ounces each.
So, Weight of x bags of lemon drops = 16x
So, Weight of (x+5) bags of lemon drops = 8(x+5)
The total weight of all the bags of candy was 400 ounces.
So, [tex]16x+8(x+5)=400[/tex]
[tex]16x+8x+40=400[/tex]
[tex]24x+40=400[/tex]
[tex]24x=360[/tex]
[tex]x=\frac{360}{24}[/tex]
x= 15
The number of bags of lemon drops are 15
The number of bags of beans =x+5 =15+5=20
Hence a system of equations that allows you to solve for how many bags of each candy Oscar bought is [tex]16x+8(x+5)=400[/tex] and The number of bags of lemon drops and number of bags of beans are 15 and 20 respectively
6. Margit works in a factory. She receives a salary of $15 per hour and piecework pay of 17 cents per
unit produced. Last week she worked 38 hours and produced 755 units.
a) What was her piecework pay?
Answer:
755*17 cents=12835 cents= 128.35$
Step-by-step explanation:
Margit's piecework pay is calculated by multiplying the number of units she produced (755 units) by the pay she receives per unit (17 cents). Therefore, her piecework pay was $128.35 for last week.
Explanation:To find out Margit's piecework pay, we need to multiply the number of units she produced by the pay she receives per unit. In this case, Margit produced 755 units and she earns 17 cents per unit. So, her piecework pay is calculated as follows: 755 units * $0.17/unit.
Therefore, Margit's piecework pay for last week was $128.35.
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at a concession stand, seven hot dog(s) and four hamburger(s) cost $18.25; four hot dog(s) and seven hamburger(s) cost $17.50. Find the cost of one hot dog and the cost of one hamburger. What is the cost of one hot dog?
The cost of one hot dog is $1.75
The cost of one hamburger is $1.5
Step-by-step explanation:
Let,
The cost of hot dog be 'x'.The cost of hamburger be 'y'.The equations can be formed as :
7x + 4y = 18.25 --------(1)
4x + 7y = 17.50 --------(2)
Multiply eq (1) by 4 and eq (2) by 7,
28x + 16y = 73
- (28x + 49y = 122.5)
- 33y = - 49.5
y = 49.5/33
y = 1.5
The cost of one hamburger is $1.5
Substitute y=1.5 in eq (1),
7x + 4(1.5) = 18.25
7x = 18.25 - 6
x = 12.25/7
x = 1.75
The cost of one hot dog is $1.75
Which statement decribes the ratio 13:8?
A
For every 8 red roses in a bouquet, there are 13 white roses.
B
For every 8 problems Nathan got correct, he got 13 incorrect.
C
For every 13 votes that Shawn received, Gayle received 21 votes.
D
For every 13 passes thrown to Harrison, he catches 8 of them.
Answer:
D
Step-by-step explanation:
that what I think but not sure
Answer:
D
Step-by-step explanation:
It is D because A would be 8:13, B would also be 8:13, and C would be 13:21. Also, we know that D is correct because for every 13 passes, Harrison catches 8 which is 13 to 8 or 13:8.
Solve the equation
5* = 125
Answer:
x=3
Step-by-step explanation:
[tex]5^{x} = 125\\5^{x} = 5^{3} \\x=3[/tex]
Answer: 5 raised to power of 3
Step-by-step explanation:
5×5×5=125
What’s the horizontal line and vertical line?-use X=blank and Y=blank.
Answer:
Part 1) Vertical line : [tex]x=1[/tex]
Part 2) Horizontal line : [tex]y=-4[/tex]
Step-by-step explanation:
Part 1) Write the equation for the vertical line passing through the point (1,-4)
we know that
The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it
so
The x-coordinate is 1
therefore
The equation of the line is
[tex]x=1[/tex]
Part 2) Write the equation for the horizontal line passing through the point (1,-4)
we know that
The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it
so
The y-coordinate is -4
therefore
The equation of the line is
[tex]y=-4[/tex]
the 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?
Answer:
[tex]\large \boxed{2}[/tex]
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.
[tex]\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}[/tex]
Check:
[tex]\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}[/tex]
It checks.
The time taken for a journey on a motorway varies inversely as
the average speed for the journey. The journey takes 1.5 h
when the average speed is 54 miles per hour. Identify the time
taken in hours for this journey when the average speed is 45
miles per hour.
Time that will be taken at speed of 45 miles/hr is 1.8 hrs
Step-by-step explanation:
Step 1: Given the speed of the journey = 54 miles/hr and time = 1.5 hours. Find the distance of the journey using the speed formula.Distance = Speed × Time
= 54 × 1.5 = 81 miles
Step 2: Calculate the time taken for this journey given speed = 45 miles/hrTIme = Distance/Speed
= 81/45 = 1.8 hrs
What’s the algebraic expression for 8 squared
Answer:
[tex]8^2[/tex]
Step-by-step explanation:
Step 1: Convert words into an expression
What’s the algebraic expression for 8 squared
8 squared -> [tex]8^2[/tex]
Answer: [tex]8^2[/tex]
If needed, solve:
[tex]8^2[/tex]
8 * 8
64
what is c- 1/2 + 16=36
Answer:
20 1/2
Step-by-step explanation:
its 20 and a half because 16+20=36 and you just need to add a half to 20 since your taking it away
Answer:
c=20.5 or 41/2
Step-by-step explanation:
c- 1/2 + 16=36
Make C the subject
c=36-16+1/2
c=20+1/2
Using LCM
c=(40+1)/2
c=41/2
c=20.5
To check if we are correct, we substitute c with 41/2. and then both sides of the equation must be equal
c- 1/2 + 16=36
41/2-1/2+16=36
20+16=36
36=36
How can I solve 8 5/6 - 2 1/3=
pookie weighs 12 7/8 pounds. Rascal weighs 13 3/8 pounds. what is totals weight of both cats
Answer:
26.25
Step-by-step explanation:
Charlene is 8 years older than Aaron. The sum of their ages is 44. What are
their ages?
Answer: charlene:52, aaron:44
Step-by-step explanation:
Add 8 to aarons age and you find your answer
Answer:
Aaron is 18 years old
Charlene is 26 years old
Step-by-step explanation:
Aaron = A
Charlene = 8 + A
Aaron + Charlene = 44
Substitute
A + 8 + A = 44
Simplify
2A + 8 = 44
Subtract 8 from both sides of the equation
2A = 36
Divide by 2
A = 18
C = 26
Hope this was useful to you!
BRAINLIEST PLUS POINTS
over the complete assessment period, Jenny averaged 35 out of a possible 40 marks for her eight math tests. When she was checking her files, she could find only seven of the test. For these she scored 29, 36, 32, 38, 35, 34 and 39. How many marks did she score for the eighth test?
Show full working out ty
Answer: 37
Step-by-step explanation:
Let X represents the score for the eighth test
Hence ( 29+36+32+38+35+34+39+X ) ÷8 =35
243+X /8 =35
243+X =35×8
243+X=280
X = 280-243
X= 37
6. An equilateral triangular pyramid has a slant height of 8.3 inches. The
triangular base has a perimeter of 4.8 inches and an area of 1.1 square
inches. Find the surface area of the pyramid.
the surface area of the equilateral triangular pyramid is approximately 21.03 square inches.
Let's calculate the surface area of the pyramid.
The lateral area of the pyramid, which is the sum of the areas of the three triangular faces, can be calculated using the formula:
[tex]\[ LA = \frac{1}{2} \times \text{perimeter of the base} \times \text{slant height} \][/tex]
We've already determined the perimeter of the base is 4.8 inches and the slant height is 8.3 inches. Substituting these values:
[tex]\[ LA = \frac{1}{2} \times 4.8 \times 8.3 = 19.92 \text{ square inches} \][/tex]
However, this only gives us the lateral area. To find the total surface area, we need to add the area of the base. Since it's an equilateral triangle, we can use the area formula for equilateral triangles:
[tex]\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times (\text{side length})^2 \][/tex]
The side length is [tex]\( \frac{4.8}{3} = 1.6 \)[/tex] inches, so:
[tex]\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times (1.6)^2 = \frac{\sqrt{3}}{4} \times 2.56 \approx 1.1084 \text{ square inches} \][/tex]
The total surface area is then the sum of the lateral area and the area of the base:
[tex]\[ SA = LA + A_{\text{base}} = 19.92 + 1.1084 = 21.0284 \text{ square inches} \][/tex]
Thus, the surface area of the equilateral triangular pyramid is approximately 21.03 square inches.
The question probable maybe:
An equilateral triangular pyramid has a slant height of 8.3 inches. The triangular base has a perimeter of 4.8 inches and an area of 1.1084 square inches. Find the surface area of the pyramid.