According to the concept of unitary method, the number of pennies are 6.
Unitary method:
The process of finding the value of a single unit, and based on this value is called as unitary method.
Given,
Out of 150 coins, 90 are quarters. Of the remaining coins, 40% are nickels and the rest are dimes and pennies. There are 5 dimes for every penny.
Here we need to find the number of pennies in the coins.
Here we know that the total number of coins are 150, thus includes
=> Quarters + nickels + dimes + pennies = 150
Here the number of Quarters are 90
Therefore, the remaining coins are calculated as,
=> 150 − 90 = 60
Here the percent of nickels is 40, then the number of nickels is
=> 60x 40/100
=> 24 numbers
Now, the remaining coins such as dimes and pennies are
=> 60 − 24 = 36 numbers.
Here we know that, in (5 + 1) = 6 coin of dimes and pennies there is 1 penny
So, in 36 coin of dimes and pennies there are,
=>36 / 6
=> 6
Therefore, there are 6 pennies.
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Solving an Equation Involving Inverse Trigonometric Functions
sec^-1 x = csc^-1 2
The solution of the trigonometry function is 2√3/3.
What is the trigonometric function?
Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given trigonometric function is
sec^(-1) x = csc^(-1) 2
Assume that,
csc^(-1) 2 = z
→ 2 = csc z
→ 1/2 =1/ (csc z)
→ 1/2 =sin z
The trigonometry identity is [tex]\cos x =\sqrt{1-\sin^2x}[/tex].
[tex]\sqrt{1-(\frac{1}{2})^2 } =\cos z[/tex]
→ cos z = √3/2
→ sec z = 2/√3
→ sec z = 2√3/(√3×√3)
→ sec z = 2√3/3
→ z =sec^(-1) ( 2√3/3) = csc^(-1) 2
Putting csc^(-1) 2 = sec^(-1) ( 2√3/3):
sec^(-1) x = sec^(-1) ( 2√3/3)
→ x = 2√3/3
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Which inequality is equivalent to -x<8
Answer:(-7, infinite down)
Step-by-step explanation: -7,-8,-9...
If 10 pants cost 240u.m, how much will 8 pants cost?
8 pants wil cost 192 u.m.
Step-by-step explanation:1. Establish a rule of 3.10 pants ----> 240u.m
8 pants ----> x
2. Solve for x.In a rule of 3, whenever the x is located at the bottom right corner, you always have to multiply upwards and to the right, and then divide the resulting number by the number on the top left. This is the operation you need to make:
x= (8 x 240) / 10
x= 192
Check the attached image to get a better understanding of this process.
3. Conclude.
8 pants wil cost 192 u.m.
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Proportional quantities are divided into directly and inversely proportional.
Two magnitudes are said to be directly proportional
when we multiply one of them by a number, the other is multiplied by the same number, and when we divide one of them by a number, the other is divided by the same number.
Problem :
If 10 pants cost 240u.m, how much will 8 pants cost?
We have:
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \\ \bold{ Assumption \: { \rightarrow} 10 \: pants \: \rightarrow 240 \: u.m\\\sf \: \: \: \: \: \: \: \: \: Question \rightarrow8 \: pants \rightarrow \: x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
As can be seen, the number of pants and the cost are magnitudes directly proportional, and therefore, we put the + sign below the pants and the - sign above.
Therefore we will have:
[tex]\boxed{ \bold{ \: x = \dfrac{240 * 8}{10} = 192 \: u.m} }[/tex]
So the 8 pants cost 192.
in a fruit punch drink, the 3 ingredients are apple juice, orange juice and cranberry juice. If 1/3 of the drink in apple juice and 1/2 is orange juice then write the ratio of cranberry juice to apple juice to orange juice in its simplest form
URGENT
The ratio of cranberry juice to apple juice to orange juice in the fruit punch is = 1 : 2 : 3
Let the total quantity of juice is 60 ml .
Now the apple juice is 1/3 of 60 = 20 ml
The orange juice is 1/2 of 60 = 30 ml
Therefore cranberry juice = 60 -(20+30) ml = 10 ml
Now the ratio of cranberry juice to apple juice to orange juice
= 10 : 20 : 30
= 1 : 2 : 3
We can exactly find out how much of one simple quantity is included in the other by simply comparing two amounts of the same units. Ratios can be divided into two smaller groups.
One is the part to the whole ratio; the other is the part to the part ratio. The exact relationship that is between the two distinct entities or groupings is only exactly depicted by the part-to-part ratio.
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An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 400 feet of antique picket fencing are to be used to enclose the garden, find
the dimensions of the garden.
Answer:
[tex]10\sqrt{6}[/tex] feet by [tex]\frac{20}{3}\sqrt{6}[/tex] ft
Step-by-step explanation:
If the length is [tex]l[/tex], then the width is [tex]\frac{2}{3}l[/tex].
Using the formula for the area of a rectangle,
[tex]l \cdot \frac{2}{3}l=400 \\ \\ \frac{2}{3}l^2=400 \\ \\ l^2=600 \\ \\ l=10\sqrt{6}[ \\ \\ \implies w=\frac{20}{3}\sqrt{6}[/tex]
The number of men and women receiving bachelor's degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees (in thousands) is given by the equation y= 3.9x+446, and for women, the equation is y= 14.2x+316, where x is the number of years after 1970.
Answer:
if what I think you want is the number of bachelor degrees from from 1970 to 2014 for both men and women is then:
men: 617.6
women: 940.8
Step-by-step explanation:
from 1970 to 2014 it is 44 years so we plug 44 into x for both equations
Men:
y = 3.9(44) + 446
y = 171.6 + 446
y = 617.6
Women:
y = 14.2(44) + 316
y = 624.8 + 316
y = 940.8
The function y=f(x) is graphed below. What is the average rate of change of the function f(x) on the interval −9≤x≤1?
The average rate of change of the function f(x) on the interval −9≤x≤1 is of:
r = -0.2.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given by the equation presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Over the interval −9≤x≤1, the bounds of the interval are given as follows:
a = -9, b = 1.
From the graph shown by the image presented at the end of the answer, the numeric value of the function at each of these bounds is given as follows:
f(-9) = 3.f(1) = 1.Hence the average rate of change of the function on the interval is calculated as follows:
r = (1 - 3)/(1 - (-9)) = -2/10 = -0.2.
Missing InformationThe graph is shown by the image at the end of the answer.
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The function f(x) is graphed below. What is true about the graph on the interval from x = -∞ to x = a?
A teacher is four times as old as a student in 20 years the student age will be half of the teacher age how old are they now
Let the present age of student be x
Present of teacher will be 4x
After 20 years,
Age of student = x + 20
Age of teacher = 4x + 20
According to the given condition after 20 years,
x + 20 = (4x + 20)/2
x + 20 = 2x + 10
2x - x = 20 - 10
x = 10
So student's present age is 10 years while teacher's is 4 x 10 i.e 40 years.
Hope This Helps You!
Write a real world situation that could be modeled by the expression, 300+7x.
A real world situation that could be modeled by the expression, 300+7x is that Bob bought goods for $300 and then bought 6 pens that cost x dollar each.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both
In this case, Bob bought goods for $300 and then bought 6 pens that cost x dollar each. The total cost will be:
= 300 + (7 × x)
= 300 + 7x
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SUPER EASY!!!!
Given the inequality 3x ≤ 24, determine the value of x.
S:{11}
S:{8}
S:{15}
S:{34}
Answer:
The answer to the question is B or 8
Step-by-step explanation:
this is because ther is 3x meaning three time what ever the answer is and because 8x3=24 it is equal to 24 so 24 is less than or equal to 24 hence the corr6 answer is 8.
Answer:
the answer is 8
ron picked 7/10 bushels of apples ben picked 9/10 bushels of apples how many apples did they pick all together give your answer in lowest terms
1 3/5
1 1/2
1 6/10
1 3/10
Answer: 1 3\5
explanation : since the denominator of both fractions are same we can go ahead and the numerators which will make the fraction 16\10 or 8/5 (simplified) and to make this a mixed numeral 5 fits into 8 once with 3 leftover thus making 1 3/5.
hope this helps .
Please help
A waste bin is in the shape of a cylinder . The diameter of the base is 20cm and the height is 25cm . what is the volume of the waste bin.
Answer:
[tex]250\pi[/tex] cm³
Step-by-step explanation:
If the radius is 20 cm, the diameter is 10 cm.
Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.
If tan(A + B) = −2 and tan B = 3, find tan A.
Answer:
Tan a =1
Step-by-step explanation:
TRIG identity:
Tan ( a+b) = (tan a + tan b )/ (1 - tan a tan b) Sub in the given values
-2 = ( tan a + 3) / ( 1 - 3 tan a)
-2 + 6 tan a = tan a + 3
5 tan a = 5
tan a = 1
please asap will give brainliest
Violet was comparing the price of chicken breast at two stores. The equation
y = 11.38x represents the total cost, in dollars and cents, y, that it costs for
pounds of chicken breast at SuperGrocery B. At SuperGrocery A, 3 pounds of chicken
breast costs $19.11.
How much more expensive is it, per pound, to buy chicken
breast at Store B than at Store A?
The chicken breast being brought at store B is more expensive than store A as it costs $5.01 more per pound.
Given,
Violet was comparing the price of chicken breast at two stores.
The equation which represents the total cost, in dollars and cents, y, that it costs for x pounds of the chicken breast at Super grocery B is:
y = 11.38x
whereas at store A the chicken breast of 3 pounds costs $19.11.
we are asked to determine how expensive is it per pound to buy chicken breast at store B than store A.
⇒ at store B the total cost is:
y = 11.38x
check the total cost of 3 pounds of chicken breast at store B:
⇒ y = 11.38(3)
since x represents the number of pounds.
⇒ y = $34.14
at store the chicken breast of 3 pounds costs $19.11
⇒ cost difference at both stores for simillar quantity:
⇒ 34.14 - 19.11
= 15.03
The cost of chicken per pound = 15.03/3
= $5.01
Hence the chicken breast at store B is $5.01 more expensive per pound than the chicken breast at store A.
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Help please i dont know how to do this.
A 270° counterclockwise rotation about the origin is the different one
How to determine which one is different?Rotation simply means turning
In order to answer this question, you need to know some rules about rotation. They are as follows:
1. If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x)
2. If a point P, whose position vector is (x,y), is rotated 270° clockwise rotation about the origin, the position of the image P' is (-y, x). This is the same number 1
3. A 90° leftward rotation about the origin is the same as a 90° counterclockwise rotation about the origin. This is the same with number 1
4. If a point P, whose position vector is (x,y), is rotated 270° counterclockwise rotation about the origin, the position of the image P' is (y, -x). This is different from the other three.
From the graph: A(1, 2), B(2, 4), C(4, 2)
Answer for the different question: A'(2, -1), B'(4, -2), C'(2, -4)
Answer for the same three question: A'(-2, 1), B'(-4, 2), C'(-2, 4)
Therefore, a 270° counterclockwise rotation about the origin is the different one. The 4th option is the answer
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Please help me need help
The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
Given,
In the question:
The matrix is given as:
A = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] & B = [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex]
To find the AB :
Now, According to the question:
AB = [tex]\left[\begin{array}{ccc}-4&-3&5\\-5&-4&-2\\-1&-2&-4\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}3&-4&-1\\-5&-5&1\\-1&-3&2\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
The basic Addition and Multiplication:
= -4 x 3 + (-3)x (-5) + 5 x (-1) = -12 +15 -5 = -2
= (-4) x (-4) + (-3)x (-5) + 5x (-3) = 16 + 15 -15 = 16
=(-4)x (-1) + (-3) x 1 + 5x 2 = 4 - 3 +10 = 11
= (-5) x 3 +(-4) x(-5) + (-2) x (-1) = -15 + 20 +2 = 7
= (-5) x(-4) + (-4)x (-5) + (-2) x (-3) = 20 + 20 + 6 = 46
= (-5) x (-1) + (-4) x 1 + (-2) x 2 = 5 - 4 - 4 = -3
= (-1) x 3 + (-2) x (-5) + (-4) x(-1) = -3 + 10 +4 = 11
=(-1) x(-4)+ (-2)x (-5) + (-4) x (-3) = 4 + 10 + 12 = 26
= (-1) x(-1) + (-2) x 1 + (-4) x 2 = 1 - 2 +(-8) = -9
Hence, The matrix AB = [tex]\left[\begin{array}{ccc}-2&16&11\\7&46&-3\\11&26&-9\end{array}\right][/tex]
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D degrees warmer than 50 degrees is 78 degrees
Answer:
28
Step-by-step explanation:
Translate words into math -- "warmer" means +, "is" means =
So D + 50 = 78
D = 78 - 50
D = 28
40 pts GET MARKED BRAINLIEST
A committee consisting of faculty members and students is to be formed. Every committee position has the same duties and voting rights. There are faculty members and students eligible to serve on the committee. In how many ways can the committee be formed?
Answer: there are 4 ways the committee can be formed
Step-by-step explanation:
The height of a plant grew linearly over the course of a month. Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
a. Find an equation that models the height of the plant H in terms of the number of days d.
b. Determine the height of the plant after 15 days.
The equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
According to the question,
We have the following information:
Initially the plant was 2 inches tall and it grew at an average rate of change of 0.125 inches per day.
2, 2.125, ...
Now, this series will become an arithmetic progression.
Formula to find the nth term:
an = a+(n-1)d
H = 2+(d-1)0.125
H = 1.875+0.125d
Now, the height after 15 days will be:
H = 1.875+0.125*15
H = 1.875+1.875
H = 3.75 inches
Hence, the equation that models the height of the plant H in terms of number of days is H = 1.875+0.125d and the height of the plant after 15 days is 3.75 inches.
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NO CALCULATOR PORTION
Let a polynomial be defined by:
f(x) = x(x + 6)(x - 2) and
f(x) = x³ + 4x² - 12x
a. Name all zeros of the function.
Step-by-step explanation:
a polynomial of degree n (that means the highest exponent of x is n) must have n zeroes.
in our case that means 3 zeroes.
the best way to find them is to have the factorial form of the polynomial : to see how several terms are multiplied to give us the polynomial.
the first f(x) gives us exactly that (the second f(x) is just the form with all the multiplications done) :
f(x) = x(x + 6)(x - 2)
when is the product of factors 0 ?
only when at least one factor is 0.
so, let's see,
when is x 0 ? well, x = 0.
when is (x + 6) = 0 ? x = -6.
when is (x - 2) = 0 ? x = 2.
so, the 3 zeroes are
x = -6
x = 0
x = 2
if a=5, b=-2 and c=3 find the value of abc
Answer:
-30
Step-by-step explanation:
the order of multiplication doesn't matter
a*b*c = 5*-2*3 = -30
Hillary ate 2/3 of a bag of Hot Cheetos in 3/4 of an hours. How much
of the bag of Hot Cheetos will Hillary eat in 5 hours.
Answer:
40/9
Step-by-step explanation:
Write the following polynomial function in standard form. f(x)=2x-x^5+2x³ - x²-1-3x¹
Answer:
-x^5+2x³-x²-1x-1
Step-by-step explanation:
First order the terms based on highest degree or exponent.
-x^5+2x³-x²-3x¹+2x-1
Next combine like terms.
-3x¹ is simply -3x so -3x+2x = -1x
-x^5+2x³-x²-1x-1
HELP, GIVING 20 POINTS FOR THIS!!!
The statement that are correct from the graph is:
Some input values are negative.
some output values are negative.
Some input values are integers.
Some output values are integers.
From the graph:
The x value is -2,-4 that is negative.
so the some inputs are negative.
Y has values -2 ,-4 which are negative.
So the some outputs are negative.
The point values from the graph is -4,-2,0,2,4 which belong to integers.
So some input values and output values are integers.
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Write the equation in slope-intercept form. Then choose the line's slope and y-intercept from the choices. So, choose two total answers. 6x+8y=-32
Answer:
Slope = -3/4, y-intercept = -4
Step-by-step explanation:
[tex]6x+8y=-32 \\ \\ 3x+4y=-16 \\ \\ 4y=-3x-16 \\ \\ y=-\frac{3}{4}x-4[/tex]
So, the slope is -3/4 and the y-intercept is -4.
A 30-sided regular polygon has an angle measure represented as 6g°. Determine the value of g.
g = 30
g = 28
g = 180
g = 168
The value of g, for a 30-sided regular polygon has an angle measure represented as 6g° is calculated to be 28
How to find the value of gThe problem is solved using the formula for number of angles for n sided polygon
The formula is (n - 2)180
where n = number of sides
for 30-sided polygon the angles is solved as below
= (n - 2)180
= ( 30 - 2 ) * 180
= 28 * 180
= 5040
this is represented as 6g
each angle is measured 5040 / 30 = 168
6g = 168
g = 28
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Answer: 28
Step-by-step explanation: 168 is the whole polygon, so 6 times 28 is 168 therefore its correct, btw i also did the test
For the figure shown find m 1
I need help with this please help me
Answer:
Step-by-step explanation:
they are expecting you to know a few things.
first, that ∠x is asking for the interior angle of the labeled angle, here they call it 1 , so find that angle and look at the inside of the triangle, it's also referred to as the minor angle.
second, they are expecting you to know how many degrees it is around the interior or a triangle... do you know?
then , just take that number and subtract the two given numbers to find the final number , or the ∠1
got it?
find the value of f(4) for the function f(a)=7(a+2) "-7"
Answer: 35
Step-by-step explanation:
[tex]f(4)=7(4+2)-7\\\\f(4)=7(6)-7\\\\f(4)=7(5)\\\\f(4)=35[/tex]