The quotient of 5 divided by 3/10 is equal to 50/3
How to divide by a fraction?When we want to divide by a fraction, we just need to replace that division by the product with the inverse of the fraction.
So, if we want to divide A by the fraction (b/c), then we can write:
A÷(b/c)
That will be equal to A*(c/b), so:
A÷(b/c) = A*(c/b)
Here we want to divide 5 by 3/10, then we need to solve:
5÷(3/10)
Using the above rule we will get:
5÷(3/10) = 5*(10/3) = 50/3
That is the quotient.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
n=4;
i and 2i are zeros;
f(-1)=20
f(x) = ?
(Type an expression using x as the variable. Simplify your answer.)
The polynomial satisfying the given conditions is given as 2x⁴ + 10x² + 8.
What is a polynomial?The polynomial is an algebraic expression in which no any terms has the power other than a whole number.
The degree of a polynomial is the highest power of one of its terms.
Given that,
The degree of polynomial is n = 4.
The zeros of the polynomial are i and 2i.
And, f(-1) = 20
Since, a polynomial with real coefficients have either real zeros or complex conjugate zeros.
Here, the given zeros of the polynomial are imaginary which implies that the remaining two zeros are the conjugate of the given two zeros.
Thus, the zeros of the given polynomial are i, 2i, -i and -2i.
The general form of a 4th degree polynomial is given as,
ax⁴ + bx³ + cx² + dx + e
Use the factor theorem to get,
ax⁴ + bx³ + cx² + dx + e = K(x - i) (x - (-i)) (x - 2i) (x- (-2i)) (1)
⇒ ax⁴ + bx³ + cx² + dx + e = K(x² + 1) (x² + 4) (2)
Now, f(-1) = 20 which gives,
K((-1)² + 1) ((-1)² + 4) = 20
⇒ k = 2
Substitute K =2 in equation (2) to get,
ax⁴ + bx³ + cx² + dx + e = 2(x² + 1) (x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2(x⁴ + 5x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2x⁴ + 10x² + 8
Hence, the nth-degree polynomial function with real coefficients satisfying n = 4 and zeros i and 2i is 2x⁴ + 10x² + 8.
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can you graph x+y greater than or equal to 500
A graph of the given inequality (x + y ≥ 500) is shown in the image attached below.
What is a graph?In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical axes of a cartesian coordinate, which are the x-coordinate and y-coordinate.
Next, we would translate the word sentence into an inequality as follows:
x + y greater than or equal to 500 ⇒ x + y ≥ 500
Subtracting x from both sides of the inequality, we have the following equation:
x + y - x ≥ 500 - x
y ≥ 500 - x
Rearranging the equation in slope-intercept form, we have:
y ≥ -x + 500
In conclusion, we can reasonably and logically deduce that both the x-intercept and y-intercept of this linear inequality (equation) is equal to 500.
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find the smallest value of an expression
(without using a calculator)
[tex]\bf\sqrt{(x-8)^2+(y+4)^2} +|y+3x|[/tex]
Step-by-step explanation:
to eliminate the always positive absolute value at the end let's set y = -3x
that makes the absolute value term = 0 in all cases.
then we have
sqrt((x - 8)² + (-3x + 4)²)
the x-value that makes this a minimum result also makes
(x - 8)² + (-3x + 4)²
a minimum.
x² - 16x + 64 + 9x² - 24x + 16
10x² - 40x + 80
the x that makes this a minimum, also makes
x² - 4x + 8
a minimum.
we get the extreme value as zero of the first derivative :
0 = 2x - 4
4 = 2x
x = 2
so, we get the minimum of all these expressions for x = 2.
as y = -3x, we get y = -3×2 = -6.
the minimum value for the expression is with
x = 2
y = -6
so, the minimum value is
sqrt((2 - 8)² + (-6 + 4)²) + |-6 + 3×2| =
= sqrt((-6)² + (-2)²) + |-6 + 6| =
= sqrt(36 + 4) + 0 =
= sqrt(40) = 6.32455532...
Differentiate the function with respect to x.
When we differentiate the given function with respect to x we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
what is Differentiation?
Differentiate is used for calculating rates of change.
How to Differentiate function?
Some of the formulas are; Power Rule: (d/dx) (xn ) = nxn⁻¹. Derivative of a constant, a: (d/dx) (a) = 0.
Here, we have
y = 2x⁵ + 2x⁴ / 5x² -3
when we differentiate a given function with respect to x, we get
dy/dx = {(5x² -3)(10x⁴ + 8x³)} - {(2x⁵ + 2x⁴)(10x -3)}/(5x -3)²
dy/dx = (30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
Hence, after differentiating the given function with respect to x, we get
(30x⁶ + 20x⁵ - 30x⁴ - 24x³)/ (5x²-3)²
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Emi is a veterinarian. In a given week, 50% of the 16 dogs she saw were boxers. Antonio is also a veterinarian. In the same week, 7 of the 35 dogs he saw this week were Boxers. Each wants to record the part, the whole, and the percent.
Emi will need to locate the whole in this case because she already has the part and the percentage.
What is a whole?In mathematics, the total number of items being analyzed, in this case, the total number of dogs, is represented by a whole.
The term "part" refers to a quantity that is typically smaller than the total and describes particular qualities. For instance, 20 of the 30 students in a classroom enjoy playing basketball. The part is 20 then.
The relationship between the part and the whole is represented by the percentage, which is a number followed by the symbol%. In this instance, the proportion of boxers and overall dogs are related.
Emi already knows the percentage (50%), the part (16), and the total number of dogs, which in this case is 32, as a result of this.
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A boy paid $11
for a bottle with a cork.
A bottle costs $10
more than a cork.
How much does a cork cost?
Step-by-step explanation:
A boy paid $11 for a bottle with a cork. A bottle costs $10 more than a cork. How much does a cork cost?
cork: c
bottle: 10c
c + 10c = 11
11c = 11
c = $1
A cork costs $1
A Finnish registration consists of 3 letters and 3 numbers with empty spaces possible.
Numbers do not have leading zeroes and the number part cannot be only zero (for example AAA-001 isn't a valid plate but AAA-1 is). The registration plate must have at least one letter and one number. How many possible Finnish registration plates are possible to exist when the letters used are the 26 letters of the latin alphabet?
Answer:
How many possible plates there could be if we also allowed the letters Å, Ä and Ö?
Answer:
Using the Fundamental Counting Theorem, the number of plates for each case is obtained as follows:
Latin Alphabet: 17,558,424.Extra Letters: 24,364,611.What is the Fundamental Counting Theorem?The Fundamental Counting Theorem is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
With the Latin letters, it is found that for the letters, there are 26 outcomes, hence:
[tex]n_1 = n_2 = n_3 = 3[/tex]
With one number, the number of outcomes for the digit is:
[tex]n_4 = 9[/tex]
(as the digit cannot be zero).
With two numbers, the number of outcomes for the digit are:
[tex]n_4 = 9, n_5 = 10[/tex]
With three numbers, the parameters are:
[tex]n_4 = 9, n_5 = 10, n_6 = 10[/tex]
Hence the total number of plates is obtained as follows:
T = 26³ x (9 + 9 x 10 + 9 x 10 x 10) = 17,558,424.
With the extra letters, each letter can assume 29 outcomes, hence the number of plates is:
T = 29³ x (9 + 9 x 10 + 9 x 10 x 10) = 24,364,611.
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The quotient of 8 and the cube of a number.
By using division, it is obtained that
The Quotient of 8 and cube of 2 is 1
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division.
Divisor x Quotient + Remainder = Dividend.
Let the number be 2
cube of 2 = [tex]2^3 = 8[/tex]
Quotient of 8 and 8 = [tex]\frac{8}{8}[/tex] = 1
The Quotient of 8 and cube of 2 is 1
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Solve: √x-4= -2
a) x=2
b) x=8
c) There is no solution.
d) x=0
The solution of the square root equation is x = 8
What is a square root?A square root is a number such that when multiplied by itself, it gives another number.
The square root of a number x is given by √x
How to solve the square root equation?Given the square root equation above, we have that
√(x - 4) = - 2
To solve this equation, first, we remove the square root by squaring both sides of the equation. So, we have that
√(x - 4) = - 2
√(x - 4)² = (- 2)²
x - 4 = 4
Adding the number 4 to both sides of the equation, we have that
x - 4 + 4 = 4 + 4
x + 0 = 8
x = 8
So, the solution of the equation is x = 8
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5 pounds=______ounces
Answer:
Step-by-step explanation:
1. Basic systems in fluids: 1 pound equals 16 ounces.
2. Multiply 16 ounces by 5 to become equivalent!
16 ounces*5= 80 ounces!
3. Always double check
80 ounces/16=5 pounds
Answer: 80 ounces
A Calculator salesman’s monthly income is $1500 salary plus a commission of 7% of his sales over $5000 what was his income the month that he sold $11,470 in calculators
$142428 income earned. A sales commission is a payment made to an employee after they successfully complete a task, typically selling a predetermined volume of goods or services.
What is commission?A type of variable-pay compensation for goods or services sold are commissions. Salespeople are frequently encouraged and rewarded with commissions. Additionally, commissions can be created to promote particular sales habits. For instance, commissions may be decreased while providing significant discounts.
Let X be the sales for a man
so7% of sales=7x/100
Total that needs to be earned=$11470
So,
Total needs to be earned= salary +commission on sale
11470=1500+7x/100
11470-1500=7x/100
9970=0.7x
X=9970/0.7
X=142428
Therefore $142428 income earned .
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Find the average for the set of numbers 7, 6, 12, 5, 7, 6, 13. Average:
Answer:
Add up all the numbers and divide the product of that by the numbers there are.
7+6+12+5+7+6+13 = 56
There are 7 numbers in these set of numbers hence we divide the product (56) by 7.
56/7 = 8
The answer is 8; The average of all these numbers is 8.
Step-by-step explanation:
Two customers went to a sports shop to buy baseball gloves. Each baseball costs the same amount, and each glove costs the same amount.
The first customer paid $60.00 for 4 baseballs and 2 gloves.
The second customer paid $84.00 for 5 baseballs and 3 gloves.
What was the cost, in dollars, of each baseball?
Question 7 options:
$8.50
$6.00
$5.25
$12.00
Hurry!!
The cost, in dollars, of each baseball is B. $6.00.
How to calculate the cost?The first customer paid $60.00 for 4 baseballs and 2 gloves. This will be expressed as:
4b + 2g = 60
The second customer paid $84.00 for 5 baseballs and 3 gloves. This will be:
5b + 3g = 84
Collect both expressions
4b + 2g = 60
5b + 3g = 84
Multiply equation i by 3
Multiply equation ii by 2
12b + 6g = 180
10b + 6g = 168
Subtract
2b = 12
Divide
b = 12/2
b = 6
The baseball is $6.
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Sixth grade > P.9 Add and subtract rational numbers GDR Add.
[tex] \frac{ - 3 \10{ + }{ - 9 \times \ \frac{910}{?} {?}{?} ?} {?} [/tex]
-
[tex] \frac{ - 3}{10 } + - 9 \times \frac{9}{10} =[/tex]
The result of the expression (-3/10) + -9 × 9/10 is -42/5
The expression is
(-3/10) + -9 × 9/10
The expression is the mathematical statement that consist of different variables, numbers and the mathematical operators.
The expression is
(-3/10) + -9 × 9/10
Here we have to do the suitable arithmetic operations
First do the multiplication in the given expression
= (-3/10) + (-9×9)/10
= (-3/10) + -81/10
Add the terms in the expression
Here the denominator of the both term is equal so we just need to add the numerators
= (-3 + -81) / 10
= (-3 - 81) / 10
= -84 / 10
Divide both numerator and denominator by 2
= -42/5
Hence, the result of the expression (-3/10) + -9 × 9/10 = -42/5
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Write 3.278 correct to 1 decimal place.
Answer: 0.3278
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!
At a fast food restaurant, customers are asked if they want to "round up" their bill to the next highest dollar and
donate the additional money to charity. The cashier is instructed to tell the customer that their bill is X dollars and Y
cents. Assume that the values of Y are equally likely to be any value from 0 to 99 cents and that customers are equally
likely to "round up" regardless of the amount of their bill. The density curve below models Y, the donation amount.
(a) What is the shape of the distribution of donations?
Amount of donation (cents)
(b) What proportion of donations are at least 75 cents?
(a) The shape of the distribution of donations is rectangular.
(b) The proportion of donations are at least 75 cents id 0.24
(a)The density curve is rectangular in shape.
This indicates that donations are distributed uniformly.
(b) From the question, we have
The probability of donations at least 75 cents as follows:
[tex]P(X\geq 75) =\int\limits^a_b {\frac{1}{99-0} } \, dx \\[/tex]
Substituting the limits, we get
[tex]P(X\geq 75) =\frac{99-75}{99} \\=\frac{24}{99} \\=0.24[/tex]
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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Find the value of the expression:
3x^0 for x=2.6
Answer:
1
Step-by-step explanation:
We don't even need to calculate 3 x 2.6 considering any number raised to the power of zero equals 1.
Amanda has 5 office assistants. If A is the event that at least 4 of them are men and B is the event that at least 4 of them are women, are A and B mutually exclusive?
Choose the correct answer below.
O No
Yes
A and B are mutually exclusive events
The correct answer is yes
What are mutually exclusive events?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously. A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.
We are given that Amanda has 5 office assistants.
Events A is the event that at least 4 of them are men. this means that there is at most 1 female assistant
Events B is the event that at least 4 of them are women. this means that there is at most 1 male assistant.
Now one of the conditions is possible but both at the same time is not possible
Hence the both events are mutually exclusive.
The correct answer is yes
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Which equation is equivalent to the given equation
x = x² - 20
A) x^2 - x-20=0
B) x^2 +x -20 =0
C) x^2-x+20=0
D) x^2+x+20=0
A company's policy is to spend no more than $350,000 a year for salaries. The president's salary is $110,000. The salaries of the eight other employees are equal. How much can be spent on each salary?
Express 6 + √ − 81 as a simplified complex number
The given algebraic expression can be simplified as 6+9i.
Complex NumberA complex number is represented by the following form: a+bi, where a and b are real numbers. The variables: a is the real part and bi imaginary part. See an example: 7 + 14i , then:
7 real part14i imaginary partRegarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 2i² = 2*(-1)= -2.
When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:
(5 + 2i) + (5 + 2i) = 10+4i
(4 + 9i) - (1 + 5i) = 1+4i
Therefore, the result for the 6 + √− 81 will be:
6+ √81i²
6+9i
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what is the momentum of an automobile with a mass of 1200 kilograms moving at 6 meters per second
The momentum of the automobile is 7200 kgm/s
What is momentum?
Momentum can be described as the product of the velocity and mass of an object.
It is a vector quantity which is defined as a quantity having both magnitude and direction.
The formula for calculating momentum is expressed as;
p = mv
Where;
p is the momentum of the objectm is the mass of the objectv is the velocity of the objectNow, let's substitute the values
p = 1200(6)
expand the bracket
p = 1200 × 6
Multiply the values
p = 7200 kgm/s
Hence, the value is 7200 kgm/s
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The scale on a map states that 1 centimeter corresponds to 15 kilometers Find how far apart two cities are if their corresponding points on the map are 13 centimeters apart
In this case, they are both centimetres, so they remain constant. The true size, 15km, is then multiplied by 13/ 1. Then, 20 × 13 = 195. As a result, the answer is 195 kilometres.
What is scale?The term scale refers to the relationship that exists between a measurement on a model and the corresponding measurement on the actual object. A scale of 1:5 means that the size of one unit in the drawing represents five units in reality. A scale of 1:5 is used, for example, if a giraffe with a real-world height of 150 inches is represented as 30 inches on the drawing. A ratio, such as 1:100, is used to represent a scale.A drawing at a scale of 1:100 indicates that the object is 100 times smaller than it would be in real life. You could also say that one unit in the drawing equals one hundred units in real life.Therefore,
The map has a scale = 1 cm
Corresponds to = 15 kilometers
Map centimeters apart = 13 cm
Then you simply multiply the true size
= 15km, by 13/ 1.
Then, 20 x 13 = 195.
Hence, the answer is 195 kilometers.
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please help 25points, please show how you did it
Answer:
Angle 1: 27
2: 153
3: 58
4: 138
Step-by-step explanation:
1. 180-(116+37)=27
2. 180-27=153
3. 180-(48+74)=58
4. 122+16=138
180-138=42
180-42=138
Solve the equation for y in terms of x
8x=1-3y
enclose numerator and denominators in parentheses
The value of y in the equation in term of x is y= (1-8x)/(3)
What are algebraic equations?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. For example, 8x = 1-3y is an algebraic equation with two variables x and y with coefficient 8 and 3 respectively and 1 is the constant.
The value of y can there be solved by firstly making 3y the subject of formula
3y= 1-8x
dividing both sides by 3
3y/3= (1-8x)/3
therefore y= (1-8x)/(3)
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Johnny recently hired a cleaning company to clean his home. The cleaning company charges
a service fee of $46 and $12 for each cleaning visit. Johnny has a monthly cleaning budget of
$130. How many cleaning visits can Johnny afford? answer?
10. Reduce the fraction 36/48 to its lowest terms.
O A. 114
O B. %
O C. 112/48
O D.34
Answer:
if D is 3/4 then it is the answer
Step-by-step explanation:
Because both 36 and 48 can be divided by 12 and 36/12 = 3 and 48/12=4 so the answer is 3/4
To serve 1 person at a local restaurant, it takes 10 minutes. To serve 5 people, it takes 18
minutes. Write and solve an equation to find the number of minutes it will take to serve a party of 8.
Answer:
8 people=24 minutes
Step-by-step explanation:
(1,10)(5,18)=18-10/5-1= 8/4 =2
y-8=2(x-4)
The population of a small town, P, as a function of time, t, in years past 1940 is given below.
P = 2,511 + 500t
For which of the following years was the population of the town 11,511?
A. 1928
B. 1958
C. 1968
D. 1918
The year for which the population of the small town is 11,511 is; Choice B; 1958.
Function evaluationIt follows from the task content that the year for which the population of the small town in discuss becomes 11,511 be determined.
Given the function: P = 2,511 + 500t
11,511 = 2511 + 500t
9,000 = 500t
t = 9,000 / 500
t = 18 years.
Hence, the year in which case the population of the small town is; 11,511 is; 1940 + 18 = 1958.
Therefore, the year in which the population of the small town in discuss becomes 11,511 as required in the task content is Choice B; 1958 is correct.
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You might need: Calculator
Solve for a.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
4x +49x+8
