a) The greatest number of students who will get the refreshment is 210.
b) Each student will get 0.5 hot dogs.
c) Each student will get 0.6 cans of fruit juice.
a) To find the greatest number of students who will get the refreshment , we need to find the least common multiple of hot dogs and fruit juice.
The least common multiple is 210, which is the multiple of 105, and 126 is the least.
So the greatest number of students who will get the refreshment is 210.
b) To find the number of hot dogs each student will receive, we need to divide the total number of hot dogs (105) by the greatest number of students who will get the refreshment (210)
105/210 = 0.5
So each student will get 0.5 hot dogs.
c) To find the number of fruit juices each student will receive, we need to divide the total number of fruit juice (126) by the greatest number of students who will get the refreshment (210)
126/210 = 0.6
So each student will get 0.6 cans of fruit juice.
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Bob made 15,000 in taxable income lat year. Suppoe the income tax rate i 15% for the firt 8000 plu 19% for the amount over 8000. How much mut Bob pay in income tax for lat year?
Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.
What is taxable income?The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.
Define revenue.Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.
The first $8000 of Bob's taxable income is taxed at 15%:
Tax on first $8000 = $8000 * 0.15 = $1200
The remaining $7000 of Bob's taxable income is taxed at 19%:
Tax on remaining income = $7000 * 0.19 = $1330
Total tax = $1200 + $1330 = $2530
So Bob must pay $2530 in income tax for last year.
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Factor the expression completely.
x^4-15x^2+54
Answer:
x^2(x^2 - 15) + 9(x-6)(x+1)
Step-by-step explanation:
To factor the expression x^4 - 15x^2 + 54 completely, we need to find the common factors in each term. In this case, we can see that the terms x^4 and -15x^2 share a common factor of x^2. To factor this out, we can use the difference of squares factorization:
x^4 - 15x^2 + 54 = x^4 - 15x^2 + (9x^2 - 9x^2) + 54
= x^2(x^2 - 15) + 9(x^2 - 6)
= x^2(x^2 - 15) + 9(x-6)(x+1)
Since x^2-15 can't be factored further. The expression is fully factored.
We can check this by multiplying it back and it should be the same as original expression.
HELP DUE IN 10 MINS!
Determine which of the following quadrilaterals have the property below. Choose all that apply.
Diagonals are congruent??
Parallelogram
Rhombus
Rectangle
Square
Kite
Isosceles Trapezoid
Answer:
Step-by-step explanation:
Of that list, only the square and the rectangle have the property you are asking for.
Try drawing it. The parallelogram has a shorter diagonal from the two obtuse angles than the diagonal from the two acute angles.
The rhombus has the same property as the parallelogram.
The kite has a far longer diagonal from the angle enclosed by the two long sides going to the angle enclosed by the two shorter sides, than a line going from the angle enclosed by one shorter and one longer side to the other angle made the same way.
what is h over 7.5 = 3.2
Answer:
h = 24
Step-by-step explanation:
h ÷ 7.5 = 3.2
Multiply both sides by 7.5
h = 3.2 × 7.5
h = 24
Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p?
In order to use the Normal approximation for the sampling distribution of p
the sample should have at least 10 successes and at least 10 failures.
What is sampling distribution?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or the mode of a variable.
What are statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
For a sample of size n = 125,
The condition for the sample size to be large enough is that both np and n(1-p) should be greater than or equal to 10. This means that the sample should have at least 10 successes and at least 10 failures. If this condition is met, we can use the Normal approximation for the sampling distribution of p.
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Regan has Rs.10,000 in total. He lent a part of it to Sandip and the remaining to Saline. If Saline paid Rs.2160 more interest than Regan at the end of 3 years and at the rate of 18% simple interest rate. Find how much money did Regan give to Sandip and Saline. (Assume 365 days in a year)
The Rs. 10,000 Regan lent to Sandip and Saline and the Rs.2160 more interest Saline paid than Sandip after 3 years at an 18% simple interest rate, indicates by expressing the amounts using equations, that the amount Regan gives to Sandip and Saline is Rs. 3,000 and Rs. 7,000 respectively.
What is an equation?An equation is the presentation of a statement of the equivalence between quantities, or expressions, by joining the expressions with a '=' sign.
The amount Regan has = Rs. 10,000
Let x represent the amount Regan lent to Sandip, we get;
The amount Regan lent to Saline = 10,000 - x
The interest rate of the loan Regan lent to Sandip and Saline = 18% simple interest
The interest Saline paid to Regan after 3 years, using simple interest = Rs. 2160 + The interest Saline paid to Regan
The simple interest formula is; I = P·R·T/100
Where;
P = The principal amount loaned
R = The interest rate = 18%
T = The time or duration of the loan = 3 years
Therefore;
(10000- x) × 18/100 × 3 = 2160 + x × 18/100 × 3
5400 - 0.54·x = 2160 + 0.54·x
5400 - 2160 = 0.54·x + 0.54·x = 1.08·x
3240 = 1.08·x
x = 3240 ÷ 1.08 = 3000
The amount Regan lent to Sandip, x = Rs. 3000
The amount Regan lent to Saline = 10,000 - x
x = 3000
10,000 - x = 10,000 - 3000 = 7,000 (substitution property)
The amount Regan lent to Saline = Rs. 7,000
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Can someone help me do this given and prove thing if u seen it and know how to
Point P is the centroid of △ABC and BD⊥AC. Find the following:
1. Find PD.
2. Find AP.
3. Find FC.
4. Find AC.
5. Find the perimeter of △BDC
Therefore , the solution of the given triangle comes out to be AC = 10 units and PD = 6 units.
Triangle definitionTriangles, which have three sides and three angles, can be made by joining any three points in a plane. They are among the earliest geometric shapes to be studied. Triangles are especially important since they may be divided into each polygon, whether it has four, five, six, or n sides.
Here,
Let AD and DC are 2x and x respectively.
We have, BC = 10 units
=> 2x =10
=> x = 10/2
=> x= 5
Now ,
=> AP + PF = 8 + y
=> 8 + y = 12
=> y =4
Therefore , the solution of the given triangle comes out to be AC = 10 units and PD = 6 units.
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Evaluate the expression 2(b+4), when b=5
The evaluation of the expression 2(b + 4) when b = 4 is 18
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
Expression: 2(b + 4)
Values: b = 5
Substitute the known values in the above equation, so, we have the following representation
2(b + 4) = 2 * (5 + 4)
Evaluate the products
This gives
2(b + 4) = 10 + 8
Evaluate the like terms in the equation
So, we have the following representation
2(b + 4) = 18
Using the above as a guide, we have the following:
The solution is 18
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Triangle GHI is dilated by a scale factor
of 4 to 7 to create triangle RST. If the
perimeter of triangle RST is 28 cm,
what is the perimeter of triangle GHI?
Answer:
It would be 49 cm
Step-by-step explanation:
Knowing the the perimeter of Tri RST is 28 cm and that it is a dilated by a 4:7 Scale Factor from Tri GHI:
(4/7)x = 28cm
(4/7)x (7/4) = 28cm (4/7)
x = 49cm
Hope that helps.
Look at image to answer
Answer:
Answer is 600!
Step-by-step explanation:
What the answer? help me out! hurry!!
A line has a slope of - 1/7 and passes through the point (4,5). What is its equation in point-slope form??
Answer:
Step-by-step explanation:
y - 5 = -1/7(x - 4)
y - 5 = -1/7x + 4/7
y - 35/7 = -1/7x + 4/7
y = -1/7x + 39/7
What is the perimeter of a rectangle with length
(3x+2) and width (x-7)?
Find the value of x in the triangle shown below. 56, 4.5, 4, 4
Answer:
x = 68°
Step-by-step explanation:
This is an isosceles triangle, which means the two base angles will be the same. (56° and 56°)
All triangles angles must add up to 180, so if we take 180-56-56 we will find the missing angle (x).
180-56-56 = 68
x = 68°
Andrew buy 8 pound of apple for $12. 0. He want to know and ue the unit rate of the cot per pound. True or Fale: Two pound of apple cot more than $3. 50
It is false that the cost of two pounds of apple cast is more than $ 3.50.
Finding the cost of a given quantity:Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.
Given that
Andrew buy 8 pounds of apples for $ 12.00
Let 'x' be the cost of 1 pound of apples
By the given data,
=> 8x = $ 12
=> x = 12/8
=> x = 1.5
The cost of 1 pound of apples = $ 1.5
Cost of 2 pounds apples = 2 × 1.5 = 3
Therefore,
It is false that the cost of two pounds of apple cast is more than $ 3.50.
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Which planes contain point W? Select all that apply.
Multiple select question.
cross out
A)
plane B
cross out
B)
plane VWY
cross out
C)
plane VWX
cross out
D)
plane m
cross out
E)
plane RYV
cross out
F)
plane VWZ
The planes that contain point W from the given image are;
Plane V
Plane VWY
Plane RYV
How to identify planes?A coordinate plane is a graphing and description system for points and lines. A vertical y-axis and a horizontal x-axis make up the coordinate plane.
From the attached image, we see that the planes whose name contains V also contains W.
The plane B contains the line XR and the Line YV as well as the W at the line YV.
Finally, the plane m also contains line YV and obviously the same as plane RYU.
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Rover it’ 3/4 of a can of cat food each day Bobo it’ 1/2 of a can of cat food each day cat food cot five dollar for three can it i only aw three can’t fox how much doe it cot for Karen for a 60 day upply of cat food for her to count cat
this question is related to numbers and the solution is as follows,
Rover eats 3/4 can of cat food in a day.
given
in 60 days it will consume 60 x 3/4 cans = 45 cans of cat food
3 cans cost = $5 and a pack contains 3 cans
45 cans is equivalent to= 45/3
= 15 packs
15 packs cost = 15 x $5 = $75
So it will cost $ 75 to feed Rover for 60 days
Bobo eats 1/2 of a can of cat food per day
in 60 days it will consume 60 x 1/2 cans = 30 cans of cat food
3 cans cost $5 and a pack contains 3 cans
30 cans are equivalent to 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So it will cost $50 to feed Bobo for 60 days
In total, in 60 days it will cost $75 +$ 50 = $125 to feed both cats in 60 days.
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As calculated from the data we get the result as that $ 125 is required for the cat food of both the cats in a month.
We are given that in 60 days he will consume ,
60 x 3/4 cans
= 45 cans of cat food
The cost of 3 cans cost = $5
and one pack has 3 cans in it.
Therefore, 45 cans is equivalent to
= 45/3
= 15 packs
So , the cost of 15 cans will be ,
15 packs cost = 15 x $5 = $75
Therefore ,$75 is used for 60 days of cat food for Rover.
Now , we know that Bobo eats 1/2 of a can food in a day.
Therefore, in 60 days he will eat,
60 x 1/2 cans
= 30 cans of food
As we know, 3 cans cost $5 and a pack contains 3 cans
Therefore, 30 cans = 30/3 = 10 packs
10 packs will cost = 10 x $5 = $50
So , $50 is spend to feed Bobo , in a month.
Therefore , if will combine their cost we will get that ,
$75 +$ 50 = $125 is required to feed both the cats in one month.
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Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to
The volume of Pill Bluetooth Speaker is 39.78 cubic inches.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, Pill Bluetooth Speaker consists two semi sphere and cylinder.
The diameter of the cylinder and semi sphere is 2 inches. the height of the cylinder is a foot.
Radius =2/2 1 inch
We know that, the volume of semi sphere is 2/3 πr³
= 2/3 ×3.14×1³
= 2.1 cubic inches
We know that, 1 foot =12 inches
The volume of cylinder is πr²h
= 3.14×1²×12
= 37.68 cubic inches
Total volume =37.68+2.1
= 39.78 cubic inches
Therefore, the volume of Pill Bluetooth Speaker is 39.78 cubic inches.
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"Your question is incomplete, probably the complete question/missing part is:"
Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to nearest tenth.
a) Volume of the Bluetooth Speaker ______
What are all values of x that make the equation true?
What is the best explanation of irrational numbers?
The best explanation of Irrational Numbers is that , the numbers that cannot be expressed as a ratio of integers are called as Irrational Numbers .
What are Irrational Numbers ?
The Irrational numbers are the real numbers that cannot be represented in the form of a ratio ([tex]\frac{p}{q}[/tex]) . In other words, the real numbers that are not rational numbers are called as irrational numbers.
For Example : [tex]\pi[/tex] is an irrational number as [tex]\pi =3.1415925...[/tex] The decimal value in the expansion never stops at any point.
Some Property of Irrational Numbers are :
(i) The Irrational numbers consist of only non-terminating and non-recurring decimals.
(ii) The Irrational Numbers are real numbers only.
(iii) The Addition, subtraction, multiplication, and division of any two irrational numbers may or may not be a rational number.
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What is the value of x?? check attachment
Answer:
D. 25°
Step-by-step explanation:
Answer:
105
Step-by-step explanation:
50+25=75, 180-175=105
eight more than the product of a number 9 is equal to 7
Answer:
The equation you have provided is 8 + 9x = 7, where x is the unknown number.
To solve for x, you can first subtract 8 from both sides of the equation to get
9x = -1
Then divide both sides by 9
x = -1/9
So the number x is -1/9, which means that the product of x and 9 is equal to -1.
Keep in mind that this is not a natural number and it is not possible to represent the solution as a whole number.
Step-by-step explanation:
Earn 100 points for this question and a brainiest
Answer:
the answer is C
Step-by-step explanation:
[tex] \frac{7}{7} - \frac{4}{7} + \frac{2}{7} [/tex]
Step-by-step explanation:
Step 1 :-
> 7/7 - 4/7
> 7-4/7
> 3/7
Step 2 :-
> 3/7 + 2/7
> 3 + 2/7
> 5/7
Option C is correct
PLS HELP ASAP 50 POINTS!!!
Identify or mark the missing side or angle that would make triangle ABC congruent to triangle PDF by AAS
The angles that would make triangle ABC congruent to triangle PDF by AAS are ∠ ACB and ∠ PFD i.e. ∠ ACB = ∠ PFD.
What is triangle?Three straight lines coming together create a triangle. There are three sides and three corners on every triangle (angles). A triangle's vertex is the intersection of two of its sides. Any one of a triangle's three sides can serve as its base, however typically the bottom side is used.
Given:
The triangle ABC and PDF are concurrent by AAS,
The AAS concurrency required two angles and one side to be equal,
Here,
AB = PD,
∠ ABC = ∠ PDF
Now one more angle is required to be equal,
∠ ACB = ∠ PFD
Thus, the missing angle is ∠ ACB and ∠ PFD.
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Twelve times one-half of a number is thirty
six. What is the number? a. 3 b. 6 C. 8 d. 18
The number will be "6".
Let,
The number be "x".According to the question, the equation will be:
[tex]12\times \frac{1}{2}x =36[/tex]By solving the above expression, we get
→ [tex]6\times x=36[/tex]
By applying cross-multiplication, we get
→ [tex]x = \frac{36}{6}[/tex]
→ [tex]= 6[/tex]
Thus the above response i.e., "option b" is correct.
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Find the surface area and round to the nearest hundredths place when necessary.
Answer:
9.4 x 11 = 103.4
15 + 7 = 22, 22 x 5 = 110, 110 divided by 2 = 55
55 x 2 (since there are two trapezoids) = 110
5 x 11 = 55
7 x 11 = 77
15 x 11 = 165
Now we add all the areas up:
103.4 + 110 + 55 + 77 + 165 = 510.4 square feet2 is your answer.
point K is the incenter of triangle PQR. what is m
Answer:
115 degrees
Step-by-step explanation:
The incenter is where the angle bisectors of a triangle meet. So [tex]m\angle{PQK}=15^\circ \text{ and } m\angle{PQR}=30^\circ[/tex].
To find the measure of angle RKQ, we need to find the measure of angle PRQ. In the big triangle, the sum of angle measures is 180 degrees, and we know two of the angles, 50 deg and 30 deg (for a total of 80 deg). That leave 100 degrees for the measure of angle PRQ.
But RK is an angle bisector, so [tex]m\angle{KRQ}=50^\circ[/tex].
We now know two of the angles in [tex]\triangle{KRQ}[/tex], 50 deg and 15 deg. Those total 65 degrees, so [tex]m\angle{RKQ}=180^\circ - 65^\circ=115^\circ[/tex]
What is the perimeter of Justin's garden in inches? I can't find the right answer 6 yards and 8 yards its a rectangle garden pls help me
Answer:
28 yards
Step-by-step explanation:
It's perimeter so you add (6x2)+(8x2)
The x2 is because there's 2 of each side
Find the measure of the indicated angle. Need help please.
I need explanation
THANK YOU
Answer: Approximately 28 km
The more accurate, yet still approximate value, is roughly 27.995735464379
Round that however you need to.
=============================================================
Explanation:
As the diagram shows, the uppercase letters A,B,C represent the corner points of the triangle. They also represent the angles. The diagram says that:
angle A = 59angle B = 91The missing angle C is....
A+B+C = 180
C = 180-A-B
C = 180-59-91
C = 30
which we'll use later.
Convention usually has the side lengths be lowercase letters 'a', b, and c. Those lowercase letters are opposite their uppercase counterpart. We'll have side 'a' opposite angle A, then b is opposite B, and c is opposite C. This allows us to quickly label a triangle and find the missing sides and/or angles. The phrasing "solve the triangle" basically means "find all the missing sides and angles". For this problem, we're only concerned with one side.
The diagram says that side c = 14 due to it being opposite angle C.
The goal is to find side b, which is the shorter way of saying "find AC".
-------------------------
From here, we can use the law of sines to find side b
b/sin(B) = c/sin(C)
b/sin(91) = 14/sin(30)
b = sin(91)*14/sin(30)
b = 27.995735464379 which is approximate
b = 28
Side AC is roughly 28 km long.
I rounded to the nearest whole number since the "14 km" is also a whole number. Your teacher may want you to round differently.
Make sure your calculator is in degree mode.
Solve the inequality - 5(x+2) < -25
x < 3
x > -3
x > 3
Answer:
x > 3
Step-by-step explanation: