The solution is, the system represents the situation is, x+y= 20
and, 2x+3y = 48.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
Each button has a diameter of either 2 or 3 centimeters.
The combined diameters of all buttons is 48 cm.
If x is the number of 2 cm buttons,
and y is 3 cm buttons.
Kate has a collection of 20 buttons.
So, the system represents the situation is,
x+y= 20
and, 2x+3y = 48.
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Higher order thinking Akira asked 20 friends what their favorite
The circle graph for the given table is as mentioned.
What is circle graph?In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with a finite system of chords of a circle such that two vertices are adjacent if and only if the corresponding chords cross each other.
Given is a data as shown in the table.
The circle graph for the given table is attached with the answer.
Therefore, the circle graph for the given table is as mentioned.
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4. Fine the lateral area for the given cylinder. Use 3.14 pi and round to the nearest whole number.
A: 144 yd2
B: 288 yd2
C: 2,712 yd2
D: 904 yd2
(50 pts and possible brainlist!!)
Answer:
D
Step-by-step explanation:
lateral area = circumference * height
= 2π*r *24
=2π*6*24 =288π yd² = 904
0.000549 in scientific notation
Answer: 5.49 × 10-4
Step-by-step explanation:
When you move the decimal over move it over to the right by 4 units.
When you move right it is (-) negative. So you get 5.49 x 10-4.
Simplify (4s^5t*-7/−2s^-2t^4)^3. Write your answer using only positive exponents
This simplified form of given expression is: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
Now, we can multiply this result by the original expression raised to the power of 3:
(4s⁵t⁻⁷/−2s⁻²t⁴)³ * (1/(-8s⁶t¹²)) = (4s⁵t⁻⁷)³ / (-8s⁶t¹²)
Finally, we'll simplify the numerator by raising 4s⁵t-7 to the power of 3:
(4s⁵t-7)³ = (4s⁵t)³ * (-7)³ = 64s¹⁵t³ * 343 = 21952s¹⁵t³
Putting it all together, we get the abbreviated version of the given expression: 21952s¹⁵t³/(-8s⁶t¹²) = 21952 / -8 *s¹⁵t³ / s⁶t¹² = 2744 / -1 * s⁹t⁻⁹
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Find the value of z from the following diagram
The value of the angle Z will be 56 degrees.
What is an arc of circle theorem?The angles that the same arc subtends at its circumference are equal. At the circle's centre, two equal chords subtend two equal angles.
The triangle in the centre is an isosceles triangle so the two angles will be 34°.
The third angle will be calculated as:-
Central angle = 180 - 34 - 34
Central angle = 112
The measure of the angle Z will be:-
Z = 112 / 2
Z = 56°
Therefore, the measure of the angle Z suspended outside will be 56 degrees.
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The answers pleaseee I’ll give you points
a) The leash is 12.2 ft long.
b) The diagonal is 7.1m
c) The altitude is 6.1 in
How to find the length of the leash?
We can see a right triangle here, where the leash is the hypotenuse of that triangle.
Using the Pythagorean's theorem we can write:
leash = √( (10ft)² + (7ft)²)
leash = 12,2 ft
8) Remember that for a square of side length S, we have:
perimeter = 4*S
diagonal = √2*S
We know that the perimeter is 20 meters, then:
20m = 4*S
S = 20m/4 = 5m
Then the diagonal is:
D = √2*5m = 7.1m
9) For an equilateral triangle of sidelength S, the altitude is:
A = √( S² - (S/2)²)
In this case the side length is 7 inches, then:
A = √( (7in)² - (7in/2)²)
A = 6.1 in
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-find the value of the variable-
show work
SOMEONE PLEASEE HELP!!!! ASAP PLEASEEE!!!!
Step-by-step explanation:
geometric mean theorem for right-angled triangles :
height = sqrt(pq)
where p and q are the parts of side as split by the height of that side.
19.
x = sqrt(4×16) = sqrt(64) = 8
20.
y = sqrt(5×8) = sqrt(40) = 6.32455532...
21.
18 = sqrt(12y)
18² = 12y
324 = 12y
y = 27
22.
10 = sqrt(25x)
10² = 25x
100 = 25x
x = 4
23.
Pythagoras
x² = 5² + height² = 25 + 4×5 = 25 + 20 = 45
x = sqrt(45) = 6.708203932...
24.
Pythagoras
b² = 16² + height² = 256 + 6×16 = 256 + 96 = 352
b = sqrt(352) = 18.76166304...
25.
Pythagoras
27² = 16² + height² = 256 + 16(z - 16) =
= 256 + 16z - 256 = 16z
729 = 16z
z = 729/16 = 45.5625
26.
Pythagoras
x² = (8 - 2)² + height² = 6² + (8 - 2)×2 =
= 36 + 12 = 48
x = sqrt(48) = 6.92820323...
What interest could be earned by a deposit of $1,500 for 6 months at a bank that pay a 4 1/8% annual interest rate, compounded semiannually?
Answer:
Interest = $720
Balance = $9,720
Step-by-step explanation:
P = $9,000, the principal
r = 8% = 0.08, the interest rate
n = 2, semiannual compounding
After 6 months, the interest is
9000 * 0.08 = $720
The balance after 6 months is
9000 + 720 = $9720
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A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {1, 5, 6, 7, 9}
A ∩ (B ∪ C) =
{1, 5, 6, 7, 9}
{}
{1, 5, 7, 9}
Answer:
hey, what are you asking
Step-by-step explanation:
A school has a toy drive for a holiday in which students bring in toys to be donated to charity. the number of toys donated by juniors and seniors are summarized in the histograms
The standard deviation of the number of toys donated by juniors is greater than that of seniors.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.
[tex]\rm \sigma = \sqrt{\dfrac{\Sigma (x_i - \mu)^2}{n}}[/tex]
For the seniors, the mean is given as,
Mean = (5 x 2 + 35 x 2 + .... + 15 x 2) / 10
Mean = 26
Then the standard deviation is given as,
σ = √[(26 - 5)² + (26 - 5)² + (26 - 15)²] / 10
σ = 14.28
For the juniors, the mean is given as,
Mean = (40 x 2 + 25 x 2 + ....... + 40 x 2) / 10
Mean = 26
Then the standard deviation is given as,
σ = √[(26 - 40)² + (26 - 25)² + (26 - 40)²] / 10
σ = 13.19
The standard deviation of the number of toys donated by juniors is greater than that of seniors.
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The complete question is given below.
Two different workers are producing a specialized part for a machine. The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Both workers averaged 5 parts per hour. Which worker has the higher variance and standard deviation?
Worker B has the higher variance and standard deviation than Worker A.
What is standard deviation?Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data. The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ.
Given,
The number of parts produced per hour by the workers are as follows:
Worker A: 5, 4, 4, 6, 7, 5, 6, 3
Worker B: 4, 8, 1, 9, 2, 9, 4, 3
Average μ = 5
Variance = σ² = Σ(xi - μ)²/N
Variance for first worker
= [(5 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (7 - 5)² + (5 - 5)² + (6 - 5)² + (3 - 5)²]/8
= [0² + -1² + -1² + 1² + 2² + 0² + 1² + -2²]/8
= [1 + 1 + 1 + 4 + 1 + 4]/8
= 12/8
= 1.5
Standard deviation σ = √1.5
= 1.2247448713916
Variance for second worker
= [(4 - 5)² + (8 - 5)² + (1 - 5)² + (9 - 5)² + (2 - 5)² + (9 - 5)² + (4 - 5)² + (3 - 5)²]/8
= [-1² + 3² + -4² + 4² + -3² + 4² + -1² + -2²]/8
= [1 + 9 + 16 + 16 + 9 + 16 + 1 + 4]/8
= 72/8
= 9
Standard deviation σ = √9
= 3
Hence, Variance and Standard deviation of worker B are higher than worker A.
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Using the given points and line, determine the slope of the line.
(-3,0) and (2,7)
O slope = -7/5
O slope = -5/7
O slope-5/7
O slope-7/5
Answer:
slope-5\7 is the answer
Joseph has a bag filled with 3 red, 3 green, 15 yellow, and 9 purple marbles. Determine P(not red) when choosing one marble from the bag.
10%
30%
50%
90%
Answer: 90%
Step-by-step explanation:
Step 1: Calculate the total number of marbles in the bag.
3 red + 3 green + 15 yellow + 9 purple = 30 marbles
Step 2: Calculate the number of marbles that are not red.
3 green + 15 yellow + 9 purple = 27 marbles
Step 3: Calculate P(not red).
27/30 = 0.9
Answer: 90%
Answer:
the answer is answer c
Step-by-step explanation:
This meal costs 32.00. A 7%. sales tax is applied, followed by an automatic tip of 18%. What is the total with tax and tip?
The total cost of a meal costing $32 with 7% sales tax and 18% automatic tip is $40
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The sales tax is 7% and the automatic tip is 18%. If the meal costs $32, hence:
Sales tax = 7% of $32 = 0.07 * 32 = $2.24
Automatic tip = 18% of $32 = 0.18 * 32 = $5.76
The total cost = cost of meal + sales tax + automatic tip
Substituting:
Total cost = $32 + $2.24 + $5.76 = $40
The total cost is $40
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if a cupboard weighs (5y+6) more than a table. 3 cupboards and 4 tables weigh (29y+ 18) pounds in all. find the weight of the table in terms of y
The weight of the table in terms of y is 2y
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
Let z be the weight of 1 cupboard
Let x be the weight of 1 table
Z = 5y+6+x
3z+4x=29y+18
=> 4x=29y+18 - 3z
Substitute for z
4x=29y+18 - 3(5y+6+x)
= 29y+18 -15y-18-3x
4x+3x=14y
=> 7x=14y
=> x=2y
The weight of the table in terms of y is 2y
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In 1995 the size of a typical personal
computer processor was 3.8 cm x 2.9 cm.
In 2009 a smartphone processor can be
as small as 1.1 cm x 0.8 cm. How much
larger is the 1995 processor than one
found in today's phones?
The 1995 processor when compared to the processor in today's phones is 12 .5 times larger .
How to find the difference ?To find how much larger the 1995 processor is , you first need to find the area of the processors.
Area of 1995 processor:
= 3. 8 x 2 . 9
= 11. 02 cm ²
Area of 2005 processor :
= 1. 1 x 0. 8
= 0. 88 cm ²
In comparison to the 2009 processor, the 1995 processor is :
= 11. 02 / 0.88
= 12 .5 times larger
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Select the two real roots of the polynomial function
S(r) = 5 +44 - 137³-10² - 12r + 72.
Or=-6; r = 2
Or=2; r = 6
Or=-6; T=-2
Or= -1; r = 6
Or= -2; r = 1
The real roots of the polynomial function are (a) r = -6 and r = 2
How to determine the real roots of the polynomial functionFrom the question, we have the following polynomial function that can be used in our computation:
s(r) = r^5 + 4r^4 - 13r^3 - 10r^2 - 12r + 72
At the real roots of the polynomial function, the following must be true
s(r) = 0
Using the above as a guide, we have the following:
Next, we test the options
Option (a)
s(-6) = (-6)^5 + 4(-6)^4 - 13(-6)^3 - 10(-6)^2 - 12(-6) + 72 = 0
s(2) = (2)^5 + 4(2)^4 - 13(2)^3 - 10(2)^2 - 12(2) + 72 = 0
See that s(-6) and s(2) have the values of 0
Hence, the real roots are s = -6 and s = 2
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The length of a rectangle is 10yd less than three times the width, and the area of the rectangle is 77yd^2 . Find the dimensions of the rectangle.
Let's let w = the width of the rectangle. If the length is 10 yards less than 3 times the width, then the length is 3w - 10.
How do we find the area? Length times width, right?
So, we have w(3w - 10) = 77. Distributing, we get 3w2 - 10w = 77.
We need to put it all on one side, so we subtract 77 from both sides.
3w2 - 10w - 77 = 0
Now, we have to factor the left side. To do this, we multiply 3(-77) = -231. What are two factors of -231 that add up to -10? How about -21 and 11? -21(11) = -231 and -21 + 11 = -10.
This may not be how you are taught, but we are now going to split -10w into -21w + 11w and plug that into our equation.
Sooooo, now we have 3w2 - 21w + 11w - 77 = 0
Next, we are going to look at the first two terms, 3w2 - 21w. What is common between the two? 3w. Factoring out 3w, we get 3w(w - 7).
Now, the second two terms, 11w - 77. What is common? 11. Factoring out 11, we get 11(w - 7).
Putting all of that together, we now have 3w(w - 7) + 11(w - 7) = 0.
I can explain why and make it more confusing, so I'll just tell you that, since the w - 7 is the same in both parentheses, we keep that as one set of parentheses and combine what's in front into a second set of parentheses.
So, we have (w - 7)(3w + 11) = 0
Lastly, for the left side to equal 0, then either w - 7 and/or 3w + 11 has to equal 0, right?
We pull each out and set them equal to 0.
w - 7 = 0
w = 7
If we plug in 7, we get (7-7)(3(7) + 11) = (0)(21+11) = 0(32) = 0, which is what we want.
3w + 11 = 0
3w = -11
w = -11/3
If we plug -11/3 into the same equation, we'd get 0, again what we want. However, we can't have a negative length! Therefore, -11/3 is out as an answer.
Our width is 7. Since the length is 3w - 10, we plug in 7 and get 3(7) - 10 = 21 - 10 = 11.
Let's check. Length times width = 7(11) = 77. Check!
True or false for the following
1) if you add two rational numbers, you’ll always get a rational number?
2) if you multiply two rational numbers, you’ll always get a rational number
3) if you divide two rational numbers, you’ll always get a rational number
All of three statements about addition, multiplication and division of rational numbers are true.
What are irrational numbers?The square root of any nonperfect square number is an irrational number.
Complex numbers (a + ib)
Real numbers Imaginary numbers.
(a + i0) (0 + ib)
Rational numbers Irrational numbers
(perfect squares) (non-perfects squares)
Fractions.
(p/q, q ≠ 0)
Integers.
(whole nos. -: 0 to ∞)
(negative integers -: - ∞ to - 1)
(positive integers -: 1 to ∞)
The statement adding two rational numbers is a rational number is true.
The statement multiplying two rational numbers is a rational number is true.
The statement if you divide two rational numbers, you’ll always get a rational number is also true.
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For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 20 N acts on a certain object, the acceleration of the object is 5 /ms2. If the force is changed to 16 N, what will be the acceleration of the object? /ms2
The acceleration of the object when the force on the object changes to 16 N is 4 m/s²
What is the basic formula for force?The second law of motion by Newton says that the force is equal to the change in momentum per change in the time. For a constant mass, force equals the mass times acceleration, i.e. F = m x a.
Given here: A force acting on an object.
We know, The formula for force states that the force is equal to mass that is multiplied by the acceleration.
Thus we have the equation as F=m.a
Now in case 1 we have
20=m×5
m=4 kg
Again in case 2 we have
16 = 4×a
a=4 ms⁻²
Hence, The acceleration of the object when the force on the object changes to 16 N is 4 m/s²
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If you would like to make $2483 in 8 years, how much would you have to deposit in an account that pays simple interest of 8%? I really need help and would also seriously benefit if you could explain formula for it as well
Answer:
2483 in 8yrs means you multiply the two first
2483
× 8
_____
19864
so 8% of 19864
you have to divide the number by the percentage
o. 8÷ 19864= 2483
A student drinks 3 cans of Mt. Dew per day. How many cases per year does this student
consume? Hint: Start off with 3 cans/day
The student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.
What is consume?Consume is an action or process of buying or using goods or services. It is the use of a resource, typically money or time, for a specific purpose. It is the purchase of goods or services for personal use or for the use of a family, business or organization. Consumption of goods and services is the basic activity of any economy.
Assuming that there are 365 days in a year, the student would consume 1,095 cases of Mt. Dew per year. This can be calculated by multiplying 3 cans per day by 365 days, resulting in a total of 1,095 cans. Since there are 24 cans per case, the student would consume 1,095/24, or 45.625 cases of Mt. Dew per year.
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emiko makes shibori scarves and sells them for $48 each on a website for handmade goods. the expression 48s represents the total price of buying s scarves
The expression 48s represents the number of scarves (s) and its per unit (48).
What is an expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given that, Emiko makes shibori scarves and sells them for $48 each on a website for handmade goods.
Here, the expression 48s represents the total price of buying s scarves
We need to tell what 48s mean,
So,
48s here is the total cost for buying s scarves,
That mean, if we buy s scarves we will have to pay $48s
Similarly, if we will buy 4 scarves, we will pay = 48 × 4 = $192
For 10 scarves, we will pay = 48 × 10 = $480
Therefore, we can say $48 is the unit price of the scarf.
Hence, the expression 48s represents the number of scarves (s) and its per unit (48).
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The question was incomplete, so I answered for the question :-
Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves what do the parts of the expression 48s represents.
Answer:
Step-by-step explanation:
number of scarves
Price of scarves
You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
The amount that should be deposited monthly is $286.66.
What is a monthly deposit?The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.
The monthly deposit can be determined using an online finance calculator.
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
FV (Future Value) = $20,000
Results:
Monthly Deposit = $286.66
Sum of all periodic deposits = $17,199.36
Total Interest = $2,800.64
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If v = 2i- ¡ and w = xi + 31, find all numbers * for which Iv + w= 5.
Answe
Step-by-step explanation:
answer is 9
Correct
The perimeter of a square must be greater than 96 inches but less than 124 inches. Find the range of possible side lengths that satisfy these conditions. (Hint: The
perimeter of a square is given by P= 4s, where a represents the length of a side).
Express your answer in interval notation. Use decimal form for numerical values.
The range of the side of the square is 24 to 31. The interval notation is (24,31).
What is interval notation?
An interval on a number line can be represented using interval notation. It is a method of representing subsets of the real number line, in other words.
Given that, the perimeter of a square must be greater than 96 inches but less than 124 inches.
Inequality form is
96 < P < 124
Where P is the perimeter.
The perimeter of a square is P = 4s, where s is the length of the side.
Putting P = 4s in 96 < P < 124
96 < 4s < 124
Divide by 4:
24 < s < 31
The interval notation is (24,31).
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Please help I will mark Brainly
Answer: -.6, 0, .6
Step-by-step explanation: (-1,6) (0,0) (1, .6)
1/2[(x+4)(x+7)] find the area
The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
A = (1/2) × h·b
The area of the triangle is given as,
A = 1/2 [(x + 4)(x + 7)]
Simplify the equation, then we have
A = [(x + 4)(x + 7)] / 2
A = (x² + 7x + 4x + 28) / 2
A = (x² + 13x + 28) / 2
The area of the triangle in terms of 'x' will be (x² + 13x + 28) / 2.
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The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23. What are the exact values of sinθ and cosθ?
The exact value of sinθ = 15.5/23
And, The exact value of cosθ = 17/23
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The terminal side of angle θ intersects the unit circle in the first quadrant at x=17/23.
We know that;
The given parameters are represented as;
⇒ (x, y) = ( cos θ , sin θ )
Here, x = 17/23
Hence, We get;
⇒ cos θ = 17/23
Now, Using the following trigonometry identity;
⇒ cos²θ + sin²θ = 1
⇒ (17/23)² + sin²θ = 1
⇒ 289/529 + sin²θ = 1
⇒ sin²θ = 1 - 289/529
⇒ sin²θ = 529 - 289 / 529
⇒ sin²θ = 240/529
⇒ sin θ = √240/529
⇒ sinθ = 15.5 / 23
Thus, The exact value of sinθ = 15.5/23
And, The exact value of cosθ = 17/23
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What is the value of x?
Answer:
Choice A (x=9)
Step-by-step explanation:
There are 180 degrees in a triangle, as seen in the picture; the triangle shown is an equilateral triangle meaning all angles are the same; therefore, each side has to be 60 degrees. Therefore the answer we plug into 5x+15 must simplify to 60. So:
5x+15
plug in 9
= 5 (9) + 15
= 45 + 15
= 60