The result in the form of a mixed number if we multiply the numerator of the complex fraction in part D by the reciprocal that you found in part E is 8[tex]\frac{1}{4}[/tex].
What is meant by a mixed number?A whole number and a legal fraction are both expressed together as a mixed number. A number between any two whole numbers is typically represented by it. An integer (whole number) plus a correct fraction together make up a mixed number, also known as a mixed fraction (a fraction whose numerator is less than its denominator).
Pretzels, peanuts, Cheerios, and of course rice and corn Chex are all included in this mix, which is why it is called a mix. It is possible for a number to contain both an integer and a fraction. As a result of combining these two sorts of numbers, they are known as "mixed numbers."
PART D:
(33/8)/(11/4)
Reciprocal of PART E is:
11/4
Therefore, multiplying it with PART D, we get:
=((33/8)/(11/4))×(11/4)
=(33/8)×(4/11)×(11/4)
=33/8
=8[tex]\frac{1}{4}[/tex]
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How do you solve 3(x−4)=15?
Answer:
9
Step-by-step explanation:
3(x-4)=15
Use distributive property with the 3 (multiply 3 times x and 3 times -4)
3x-12=15
Add the 12 to both sides.
3x=27
divide 27 by 3.
x=9
Answer:
x = 9
Step-by-step explanation:
How do you solve 3(x−4)=15?
3(x − 4) = 15
divide both side by 3
x - 4 = 5
x = 5 + 4
x = 9
----------------
check
3(9 - 4) = 15
9 - 4 = 5
5 = 5
the answer is good
Frames-for-All sells framed pictures to hotels and other corporations across the country. Last year, the company sold a total of 720,460 pictures. This year, they sold 972,621 pictures. What is the percent of increase in yearly sales?
Therefore the percentage of increase in yearly sales is 35% by last year.
What is percentage?
Percentage refers to a number that is "out of one hundred." As with fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When utilizing percentages, the total is regarded as being composed of 100 equally sized components. In addition to the abbreviation "pct," which is used less frequently, the symbol "%" is used to denote percentages in numbers.
Here,
the company sold a total of 720,460 pictures Last year.
This year, they sold 972,621 pictures
therefore first we have to find the difference between the last year and this year pictures sold
it comes out to be,
=>972,621-720,460=252,161
Therefore the increase in percentage this year=
=> 252,161/720460 * 100
=>0.35*100
=> 35%
Therefore the percentage of increase in yearly sales is 35% by last year.
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what is the value of p
The value of p is 18, it can be find out by using concepts of line and slope of a line.
What is the slope of a line?
Slope of line measures its steepness. Mathematically, its calculated as "rise over run".
Slope of a line : (y2 - y1)/(x2-x1)
In the given que,
given graph equation is of line ,
to find slope of graph : we need to differentiate the equation
[tex]\frac{d}{dx}[/tex](3y + 2x = 7) = 3[tex]\frac{dy}{dx}[/tex] + 2 = 0
So, [tex]\frac{dy}{dx}[/tex] = -2/3
We, if any line are perpendicular then
slope of one * slope of two = -1
So, slope of 1 = (-9-6)/(8-p)
= -15/(8-p)
slope of 2 = -2/3
Now product of both = -15/(8-p) * (-2/3 )
By simplifying all these equation,
we get p = 18.
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80 of the students walk to school.
60 of the students cycle to school.
(c) Write the ratio of the number of students who walk to school to the number of
students who cycle to school.
Give your ratio in its simplest form.
Answer:
4/3 also can be written 4:3
Step-by-step explanation:
Compare numbers in the order that the question asks for them. Order matters.
walkers/cyclers
= 80/60
Simplify.
= 8/6
= 4/3
The ratio of walkers to cyclers is 4/3 (also can be written 4:3)
what is the solution to the equation 3 (2 x 5) = 3 x 4 x?x = 0x = 4x = 5
The answer to the equation 3(2x-5)=3x is 5, which corresponds to value option C first from list.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression. An expression in mathematics is made up of numbers, variables, and functions. You can think of expressions as being similar to phrases.
Here,
3(2x-5)=3x
6x-15=3x
3x=15
x=5
The solution to the expression 3(2x-5)=3x is 5 that is option C from the given choices of value.
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A college student is buying a used car for $10,000. The student can either pay in full with cash from savings, or finance the car for 60 months at a monthly compounding interest rate of 5.25%, which results in a monthly payment of $216.57.
How much more is paid over the life of the loan versus paying in cash?
O $2,994.20
O$12,994.20
O $1,082.85
O $11,082.85
Therefore, the student would pay $2,994.20 more over the life of the loan than if they paid in cash.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". Percentages are commonly used to express ratios, proportions, and rates. They are used in many areas of everyday life, such as in finance, business, and statistics. Some common examples include: Interest rates on loans and credit cards, Discounts on sale items in stores, Tax rates on income or purchases, Probability of events occurring, Performance metrics in sports and other competitions. Percentages can be converted to decimals or fractions for calculations, and vice versa.
Here,
If the student pays in full with cash, the total cost of the car is $10,000.
If the student chooses to finance the car, the monthly payment is $216.57 and the number of months is 60. The total amount paid over the life of the loan is:
Total paid = Monthly payment * Number of months
= $216.57 * 60
= $12,994.20
The amount paid over the life of the loan is the difference between the total paid and the initial cost of the car:
Amount paid over life of loan = Total paid - Initial cost
= $12,994.20 - $10,000
= $2,994.20
The correct answer is option O: $2,994.20.
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Mark did a survey.
He asked pupils in his school:
‘Do you like the colour of the school uniform?’
Mark asked this question to 40 pupils in year 11
25% said ‘Yes’. 50% said ‘No’. The rest said ‘Don’t know’.
Complete the table to show how many pupils from year 11 gave each answer.
The following numbers will be illustrated in the table:
Those that said yes = 10
Those that said no = 20
Those that said don't know = 10
How to illustrate the percentage?It should simony be noted that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Number of pupil = 40
25% said ‘Yes’. This will be:
= 25% × 40.
= 10
50% said ‘No’. This will be:
= 50% × 40
= 20
The rest said ‘Don’t know’. This will be:
= 25% × 40
= 10
In conclusion, those who said yes are 10 while those who said no are 20.
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Find x. Please give a correct answer
Answer: x = 110
Step-by-step explanation:
A 7-sided shape, also known as a septagon, has a total of 900° among its angles. We will set up an equation and solve by combining like terms and using inverse operations.
105° + 150° + 140° + x° + 135° + 125° + 135° = 900°
790° + x° = 900°
x = 110
the odds of a particular event occurring is 0.66. determine the probability as a decimal rounded to the nearest hundredth.
The probability of odds as a decimal rounded to the nearest hundredth is 0.398.
The probability of odds is given by the formula -
Probability of odds = probability odds ÷ probability (1 + odds)
Probability odds = 0.66
Probability (1 + odds) = 1 + 0.66
Performing addition on Right Hand Side of the equation
Probability (1 + odds) = 1.66
Keep the values in formula to find the probability of odds
Probability of odds = 0.66/1.66
Performing division on Right Hand Side of the equation
Probability of odds = 0.398
Hence, the probability of odds is 0.398.
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four standard six-sided dice are to be rolled. what is the probability that the product of the numbers on the top faces will be prime? express your answer as a common fraction.
The probability of the product of the numbers present on the top faces of all the four six sided dice is equal to 1/108.
As given in the question,
Number of six sided dice to be rolled = 4
Number of outcomes on one dice = 6
Total number of outcomes of 4 dice = 6⁴
= 1296
Conditions for the product of the numbers of top faces all four dice is prime:
Three dice should have 1 on the top face and fourth one should have prime number less than 6.prime number less than 6 are 2, 3, 5.Each prime number will comes on all the four dices top faces.Favourable outcomes are : ( 1, 1, 1,2), (1,1,2,1), (1,2,1,1), (2,1,1,1),
( 1, 1, 1,3), (1,1,3,1), (1,3,1,1), (3,1,1,1),( 1, 1, 1,5), (1,1,5,1), (1,5,1,1), (5,1,1,1)
Total number of favourable outcomes = 12
Required Probability = 12 / 1296
= 1 / 108
Therefore, the probability of the product of all the four numbers on the top faces of the dice is equal to 1/108.
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16 donuts in 4 boxes =
donuts in 2 boxes
Answer:
8
Step-by-step explanation:
First, divide 16 by 4 to see how many donuts are in each box. This equation gives us 4. Then, multiply 4 by 2 to see get the answer of 8.
Answer: well if there are 16 donuts in 4 boxes that means there are 4 donuts in each box
Step-by-step explanation:
4=4
4+4=8
4+4+4=12
4+4+4+4=16
so your answer is 8
simplify. express your answer using positive exponents. (2c7)(9c)
The simplified form of the given expression, (2c7)(9c), is 18c⁸
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
(2c7)(9c)
First, we will write the expression properly
The given expression written properly is
(2c⁷)(9c)
Now, we will simplify the expression
Simplifying the expression
(2c⁷)(9c)
Multiply
2c⁷ × 9c
Collect like terms
2×9 × c⁷ × c
18 × c⁷⁺¹
18 × c⁸
18c⁸
Hence, the expression is 18c⁸
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Evaluate the integral by reversing the order of integration. Double integrate e^x^2 dxdy=
the integral by reversing the order of integration. Double integrate e^x^2 dxdy= 1/3x e^x^3 + C
The integral can be written as:
∫ ∫ e^x^2 dx dy
∫ ∫ e^x^2 dy dx
Applying the formula for double integrals, the answer is:
∫ e^x^2 dy × ∫ dx
Since the inner integral is a constant, it is simply equal to x.
The answer is therefore:
∫ e^x^2 dy × x = x × ∫ e^x^2 dy
The outer integral is a standard antiderivative, and is equal to:
1/3e^x^3 + C
Therefore, the final answer is:
1/3x e^x^3 + C
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Question attached through files! Can anyone help?? Thank you!
Answer:
(-1.732,0) and (1.732,0)
Step-by-step explanation:
Ignore f(x). The solutions are also called x-intercepts and zeros. So the solutions would be where the parabola crosses the x axis. In my answer ignore the 0 in the coordinates. Just put in the -1.732 and 1.732.
Use I=PRTI=PRT to find the total amount in the savings account. Type in "money form".
$4500.00 at 8% for 3 years
The total amount earned after 3 years at 8% rate is $5580
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money.
Given that, $4500 is invested at 8% for 3 year,
SI = PxRxT/100
= 4500x8x3/100
= 1080
Amount = interest + principal
Amount = 1080 + 4500 = 5580
Hence, The total amount earned after 3 years at 8% rate is $5580
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(1,4) and (6,-1) in linear equation
y = 5 - x. is the linear equation in point-slope form.
How To find the Slope from two points ?Using the slope formula, determine the slope.To find the y-intercept (b), use the slope and one of the points.You may obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).Points (1,4) and (6,-1).
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).
where , m = slope of the line. x₁ = the x-coordinate of the first point.
m = (-1 - 4) / (6 - 1 ).
m= -1
Substitute the values into the point-slope form,
y − y 1 = m ( x − x 1 ) .
y − 4 = -1 ( x − 1) .
y − 4 = 1 - x.
y = 5 - x.
complete question : Write the linear equation in point-slope form that passes through the given points. (1, 4) and (6, -1).
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. A study was conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction. With a substrate concentration of 1.5 moles per liter, the reaction was run 15 times, with an average velocity of 7.5 micromoles per 30 minutes and a standard deviation of 1.5. With s substrate concentration of 2.0 moles per liter, 12 runs were made, yielding an average velocity of 8.8 micromoles per 30 minutes and a sample standard deviation of 1.2. Is there any reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes? Use a 0.01 level of significance and assume the populations to be approximately normally distributed with equal variances.
At the significance level, 0.01
p-Value=0.973 > 0.01 which implies fail to reject null hypothesis and no evidence to support the claim.
So, there is no reason to believe that this increase in substrate concentration causes an increase in the mean velocity of the reaction of more than 0.5 micromole per 30 minutes.
We have given that,
A study conducted to see if increasing the substrate concentration has an appreciable effect on the velocity of a chemical reaction.
x₁-bar = 8.8 micromoles
Standaard deviations, s₁= 1.2
x₂-bar = 7.5 ; s₂ = 1.5
n₁ = 12 ; n₂ = 15
significance level = 0.01
Consider the Null hypothesis and alternative hypothesis othesis
H₀ : μ = 0.5
Hₐ : μ > 0.5
Consider,
Pooled Standard Deviation = √(((n₁ - 1)s₁² + (n₂- 1)s₂²)/(n₁ + n₂-2))
plugging all known values
= sqrt(((12-1)(1.2²) + (15 -1)(1.5²))/(12+15-2))
Sp = 1.3761
Now , test statistic :
t =((x₁-bar - x₂-bar) - 0.5) / (Sp×√(1/n₁+ 1/n₂))
substitute all known values we get,
= ((8.8 - 7.5) - 0.5) / (1.3761× sqrt(1/12 + 1/15))
=> t = 1.5
Degree of freedom = n₁+ n₂ - 2
= 12 + 15 - 2
= 25
Now the p-value corresponding to t = 1.5 & df = 25 is 0.073
Here p-value > 0.01 (significance level) thus, we fail to reject null hypothesis.
So there is no enough evidence to support the claim.
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Jack sketches ΔABC. The measure of angle B is 6 degrees less than twice the measure of angle A. The measure of angle C is 111°.
Which equation can be used to find the measure of Angle A? What is the measure of Angle A?
The equation that can be used to find the measure of Angle A is (b) a + 2a - 6 + 111 = 180, a = 25
Which equation can be used to find the measure of Angle A?From the question, we have the following parameters that can be used in our computation:
Angle B = 6 degrees less than twice the measure of angle A
Angle C = 111 degrees
These mean that
b = 2a - 6
c = 111
The sum of angles in a triangle is 180
So, we have
a + 2a - 6 + 111 = 180
What is the measure of Angle A?In (a), we have
a + 2a - 6 + 111 = 180
Evalate the like terms
3a = 75
So, we have
a = 25
Hence, the equation is a + 2a - 6 + 111 = 180
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John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually. How much interest does the account earn in the first six months? What is the balance after a year.
The required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.
Given that,
John deposits $ 8,000 in a certificate of deposit that pays .8% interest, compounded semi-annually.
Investment is defined as when an individual is spend money on something that returns him or her higher money than the money they or invest.
Here,
Interest earned in the 6 months,
= 8000 [0.08/2]
= $320
Balance after a year,
Amount = principal [1 + rate/n]ⁿ
= 8000[1 + 0.08/2]²
= $8652.8
Thus, the required interest earned in the 6 months is $320 and the balance after a year is $8,652.8.
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Sam and ben are grading english tests. Sam grades 6 6 tests in 24 24 minutes and ben grades 5 5 tests in 20 20 minutes. At these rates, what is the total number of tests they can grade in 3 3 hours? enter the answer in the box.
The total number of tests graded by them in 180 minutes (3 hours) will be 90 tests.
Sam ,
6 tests in 24 mins
Therefore ,
1 test in 24/6 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Ben,
5 tests in 20 mins
Therefore ,
1 test in 20/5 = 4 mins
hence ,
no of test in 180 mins
= 180/4 = 45
Therefore at the end of 180 mins
they would have graded 45 + 45 = 90 tests.
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious.
In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers.
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find the distance between the two points, round to the nearest tenth (if necessary).
(−2,−5) and (−7,−7)
Leg 1:
Leg 2:
Distance:
The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units
What is the distance between two points?
Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )
The distance from A to B is the same as the distance from B to A
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane
Given data ,
Let the first point be A ( x₁ , y₁ )
The value of A ( x₁ , y₁ ) = A ( -2 , -5 )
Let the second point be B ( x₂ , y₂ )
The value of B ( x₂ , y₂ ) = B ( -7 , -7 )
Now , the distance between the two points is given by the formula
D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)
where D is the distance
Substituting the values in the equation , we get
Distance D = √ [ ( -7 - (-2) )² + ( ( -7 - (-5) )² ]
On simplifying the equation , we get
Distance D = √ (-7 + 2 )² + ( -7 + 5 )²
Distance D = √ ( -5 )² + ( -2 )²
So , the value of D is
Distance D = √ ( 25 + 4 )
Distance D = √29 units
So , the approximate value of distance D = 5.39 units
Therefore , the value of Distance D = 5.4 units
Hence ,
The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units
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Which value of x makes the equation 3-0.5(2x-8)=(3X+28) true
Step-by-step explanation:
In order to solve this equation, you will need to use the following steps:
First, simplify the left side of the equation by performing the operation of multiplying 0.5 and (2x-8) to get 0.5(2x-8)=x-4.
Then, subtract 3 from both sides of the equation to get x-4=3x+28.
Next, subtract 3x from both sides of the equation to get -3x+x-4=28.
Combine the like terms on the left side of the equation to get -2x-4=28.
Add 4 to both sides of the equation to get -2x=32.
Finally, divide both sides of the equation by -2 to get x=16.
Therefore, the value of x that makes the equation 3-0.5(2x-8)=(3x+28) true is 16.
has mean 20.2 years and standard deviation 1.60 years. of all of those enrolled in the course, 54 percent are men and 46 percent are women. what is the mean age of the combined distribution of both men and women in the course?
The mean age of the combined distribution of both men and women in the course is 20.47 years
What is average/mean ?
The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.
Mean age of men , M = 20.7 years
Mean age of Women , W = 20.2 years
Percentage of Men = 54%
Percentage of Women = 46%
Recall, :
Mean, μ = np
The mean age of men in the distribution = (20.7 × 54%) = 11.178 years
The mean age of women in the distribution = (20.2 × 46%) = 9.292 years
The mean age of the combined distribution is :
11.178 + 9.292 = 20.47 years
Therefore, the mean age of the combined distribution is 20.47 years
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2. The straight line y
=
5
x makes an acute angle with the x-axis when graphed.
12
a. Write down the value of tan 0.
Determine the exact values of:
b.
i. sin(20).
ii. cos(20).
iii. tan(20).
By using trigonometry, it can be calculated that-
a) tan[tex]\theta[/tex] = 5
b) i) sin(20) = 0.342
ii) cos(20) = 0.934
iii) tan(20) = 0.364
What is trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are [tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\\[/tex]
Trigonometry is a very important tool in mathematics.
Here, trigonometry will be used
a) Equation of line
y = 5x
Slope of the line = 5
So, tan[tex]\theta[/tex] = 5
b) i) sin(20) = 0.342
ii) cos(20) = 0.934
iii) tan(20) = 0.364
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what is the initial value and rate of change in y=3x-5
PLESE HELP
Answer:
the rate of change is 3x(slope)
1. After a pay raise, Kate's monthly salary increased from $3500 to $3780. Find the percentage increase in her pay raise.
Answer:
8%
Step-by-step explanation:
1. Subtract the larger number from the smaller:
3780 - 3500 = 280
2. Divide the result from step 1 by the FIRST salary amount:
280 ÷ 3500 = 0.08 NOTE: Order Matters!!!
3. Change the decimal to a percent
A direct variation includes the points (3, -18) and (-2, n). Find n. Write and solve a direct variation equation to find the answer.
n =
Using Direct Variation, the value of n = 26
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We need to Write y = kx based on the conditions stated.
Replace with: -18 = k x 3
Turn the sides around: k × 3 = -18
Now Subtract the coefficient of the variable from both sides of the equation:
k = 26 compute the product or quotient.
Write the function's equation as;
y = 26x
Replace with:
n = 26 × 4
n = 104; compute the product or quotient.
Response: n = 26
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Which of the following is not a criteria for the construction of a triangle?
A
ASA
B
SAS
C
SSS
D
AAA
Answer:
D) AAA
Step-by-step explanation:
find the common ratio.
1\text{,}2\text{,}4\text{,}8\text{,}16\text{,}..1,2,4,8,16,...
48\text{,}12\text{,}4\text{, }2\text{,}..48,12,4, 2,...
The common ratios of the sequence are 4 and 1/4
How to calculate the common ratioFrom the question, we have the following parameters that can be used in our computation:
Sequence 1
1, 2, 4, 8, 16,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 2/1
Evaluate
Common ratio = 2
Sequence 2
Here, we have
48, 12, 4, 2,...
The common ratio is the quotient of a term and the previous term
Using the first term and the second term, we have
Common ratio = Second term/First term
Substitute the known values in the above equation, so, we have the following representation
Common ratio = 12/48
Evaluate
Common ratio = 1/4
Hence, the common ratio is 1/4
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How do you simplify (−2−i)^2?
[tex](-2-i)^{2}[/tex] can be simplified by multiplying the integer by itself.
Multiply the integer by itself.
[tex](a+b)^{2} =a^{2} +2ab+b^{2}[/tex]
[tex](-2-i)^{2} =((-2)^{2}+(-i)^{2})[/tex]
Simplify
[tex](-2)^{2} +2.(-2).(-i)+(-i)^{2}[/tex]
[tex]=4+4i-1[/tex]
Make use of the property [tex]i^{2} =-1[/tex] to decrease the imaginary units.
[tex]4+2i+21i+1(-1)[/tex]
Simplify and use the a+bi formula in standard form.
[tex]3+4i[/tex]
A real number is the result of a complex number and its conjugate. This knowledge will be used to remove the complex number from the given expression's denominator.
To learn more about integers, refer:-
https://brainly.com/question/15276410
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