The standard form of the equation of the given straight line is 4x + (-7)y = 13.
We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is given below.
8x = 26 + 14y
We need to convert this equation to standard form. The standard form of an equation for a straight line is given below.
Ax + By = C
We need to rearrange the given equation so that it matches the correct format. The equation is written below.
8x - 14y = 26
We can simplify the equation further by dividing the whole equation by two.
4x + (-7)y = 13
Hence, the standard form of the equation is 4x + (-7)y = 13.
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A ratio is a comparison of two quantities. For example, the ratio of cows to pigs on a farm could be 1 to 3. For every 1 cow, there are 3 pigs. The ratio of chocolate chips to raisins in a cookie could be 5 to 9. For every 5 chocolate chips in the cookie, there are 9 raisins. Do you notice a repeating phrase in these examples? “For every” is key ratio language. It tells you how much of one quantity exists in comparison to the other quantity. A ratio consists of just the numbers, not the units. If someone asked the ratio of chocolate chips to raisins in the cookie example, you’d say 5 to 9.
Which of these could you represent with a ratio?
Answer:vvvvvvvvvvvvvvvvvv55555
Step-by-step explanation:
fill in the missing field to complete the program. determine the number of elements in the list that are divisible by 10. (hint: the number x is divisible by 10 if x % 10 is 0.) div ten
The number of elements in the list that are divisible by 10 is 10, 20, 30, 1000, 5000, 60000, etc.
Given:
the number of elements in the list that are divisible by 10. (hint: the number x is divisible by 10 if x % 10 is 0.) div ten
The number is divisible by 10 and the last digit is zero.
suppose take 10:
= 10/10 = 1
It is divisible.
= 10%10
The last digit or remainder is zero.
Therefore the number of elements in the list that are divisible by 10 is 10, 20, 30, 1000, 5000, 60000, etc.
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Multiply. Simplify the answer and write as a whole number.
7 1/2-1 1/5
The answer is in the form of whole number is 6 .
Given,
In the question:
The number is given as:
= [tex]7\frac{1}{2} - 1\frac{1}{2}[/tex]
Now, According to the question:
= [tex]7\frac{1}{2} - 1\frac{1}{2}[/tex]
Convert to fraction into mixed fraction:
= 15/2 - 3/2
Calculate the sum or difference:
= 12/2
Cross out the common factor:
= 6
Hence, The answer is in the form of whole number is 6 .
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indicate the answer choice that best completes the statement or answers the question. 1. how many different samples of size 3 (without replacement) can be taken from a finite population of size 10? a. 30 b. 1,000 c. 720 d. 120
The correct option is option (d).
Using Combination,
Total 120, different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Population size: The population is the entire group of guesses. A sample is a specific group for which you collect data. It is denoted by N.
Sample Size: The sample size is always smaller than the total size of the population. A sample is a subset of the population set. It is denoted by n.
we have given that , n = 3 and N = 10
Using the following formula for calculating the possible number of different samples of size 3 (without replacement) can be taken from a finite population of size 10.
Number of possible different samples of size n from Population size N = NCn = N!/n! (N-n)!
then we have, 10C3 = 10!/3! × 7!
=> 10×9×8/3×2 = 15×8 = 120
Hence, 120 different samples of size 3 (without replacement) is possible from Population of size 10.
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1. Evaluate-[34+ (-16)-12].
a. 16
b. -16
C.-6
16
Step-by-step explanation:
[34-16-12]
[18-12]
16
What is five and eight hundreds in standard form
Answer:5.08
Step-by-step explanation:
Does this figure have symmetry?
Answer:
Yes, because if you fold it in half, both halves match up.
Step-by-step explanation:
You can fold the figure in half along the x-axis to get a "D" shape
Decribe and correct the error in fining the um 2 5/6(-8/15)=12/6(-8/15)=65(-16)/30=49/30=1 19/30
Error free in finding the sum of 2 is 9/30
we need to correct the error and find the sum of 2
= [tex]\frac{5}{6}[/tex] + ([tex]\frac{-8}{15}[/tex])
let's find the l.c.m of both
LCM stands for 'Least Common Multiple'. The least common multiple (LCM) of two numbers is the lowest possible number that can be divisible by both numbers. It can be calculated for two or more numbers as well. There are different methods to find the LCM of a given set of numbers. One of the quickest ways to find the LCM of two numbers is to use the prime factorization of each number and then the product of the highest powers of the common prime factors will be the LCM of those numbers.
= 25 -16 / 30
= 9/30
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from a group of 10 people, a committee of 5 is to be formed. the committee consists of a chair, a secretary and 3 regular members. (a) how many dierent committees are possible?
The number of ways of selecting a committees of 5 members from a group of 10 people will be 252
Combination is a method to calculate different ways to select items from a set / group regardless of the order.
ⁿCₓ = n! / (n-x)! x!
Total number of people in group is 10
Number of people require to form committee is 5
By using Combination ,
¹⁰C₅ = 10! / (10 - 5 )! 5!
= 10×9×8×7×6×5! / 5! × 5!
Cancelling 5! from numerator and denominator
= 10×9×8×7×6 / 5!
expanding the factorial
= 10×9×8×7×6 / 5×4×3×2×1
= 252
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What is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches?.
4.8 inches is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches.
Using the formula for the area of a trapezoid, which is:
Area = (1/2)(b1 + b2)h
In this formula, b1 and b2 are the lengths of the two bases of the trapezoid, and h is the height of the trapezoid. In our problem, we know that the area is 24 square inches, and the lengths of the two bases are 4 inches and 6 inches. We want to solve for h, the height of the trapezoid.
Plugging in the known values, we get:
24 = (1/2)(4 + 6)h
24 = (1/2)(10)h
24 = 5h
4.8 = h
Therefore, the height of the trapezoid is 4.8 inches.
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Write an equation in slope-intercept form for the line that passes through (9, 12) and is perpendicular to y=4
Answer:
[tex]x=9[/tex]
Step-by-step explanation:
First, let's determine the slope! We know that the line is perpendicular to [tex]y=4[/tex]. This line is just a horizontal line that crosses the y-axis with a slope of 0. The line perpendicular to this will have the form [tex]x=?[/tex]. This is a straight, vertical line with indeterminate slope.
The line passes through the point (9, 12). If the line is going straight up and down, it will intercept every y-value, but only one x-value. The x-value in this ordered pair is 9. Therefore, the equation of the line is [tex]x=9[/tex].
a couple has 3 children. they sit in 5 adjacent seats in the same row while watching a movie. if the mother must sit in between the two youngest children, how many seating arrangements are possible?
Answer: well about 3
Step-by-step explanation:
father(youngest)mom(middle child)oldest
oldest(youngest)mom(middle child)father
father(middle child)mom(youngest)oldest
hope this helps:)
what happens to the width of two-sided confidence interval as each of these attributes changes? - the confidence level increases - the sample size increases a. increases b. decreases
The width of two-sided confidence interval decreases as the sample size increases and increases as the confidence level increases.
Confidence interval : In Statistic, confidence interval is a range of estimates for unknown parameters.
The formula for the interval can be expressed as:
Confidence Interval (CI ) = X bar +_ Z( S/√n)
Where,
X bar ---> the sample mean
S ---> the sample standard deviation
n --> the sample size Z---> Z-value which comes from normal distribution
From the formula we can conclude the below points about confidence interval :
The increases in confidence level leds to increase the width of the confidence interval also. A larger confidence level means the interval is larger. the width of confidence interval varies inversely to sample size i.e increase in sample size implies decrese in width of confidence interval. .Confidence interval increases with increase of sample standard deviationsSo, Confidence interval varies with sample mean, confidence level and standard deviations.
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the picture is my question
Answer:
[tex] \rm \implies \frac{1}{3} (5x - 8) + \frac{2}{3} x \\ \\ \rm \implies \frac{5}{3} x - \frac{8}{3} + \frac{2}{3} x \\ \\ \rm \implies \frac{5x + 2x}{3} - \frac{8}{3} \\ \\ \rm \implies \frac{7x}{3} - \frac{8}{3} \\ \\ \rm \implies 2 \frac{1}{3} x - 2 \frac{2}{3} [/tex]
Kareem Abdul-Jabbar is the all-time leader in points scored in professional
basketball. He averaged 1,919.35 points scored each season. About how many points
did Kareem score during his twenty-year career?
Kareem Abdul-Jabbar scored a total of 38387 point in his career
MultiplicationIn math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. The two factors and the product are parts of a multiplication problem. In the multiplication problem, 6 × 9 = 54, the numbers 6 and 9 are the factors, while the number 54 is the product.
To find the number of points he had in his total career, we just need to multiply his points per season with the total number of years he spent play game.
This becomes 1919.35 * 20 = 38387 points
He had a total of 38387 points all time in his career
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FLE.
= a
=t.
18. The table shows the amount of fabric
Camille used based on the number of
headbands that she made. Find the slope, and
explain what it means in the context of the
situation.
Headbands
Fabric (yd)
3
3
5
5
1
7775
5015
9
q
The slope of the line is 1/5 and it means the each headband uses 1/5 yards of fabrics
First choose two points
The first point = (3, 3/5)
The second point = (5, 1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where [tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line = (1- 3/5) / (5 -3)
= (2/5) / 2
= 1/5 yards per headband
Hence, the slope of the line is 1/5 and it means the each headband uses 1/5 yards of fabrics
The complete question is
The table shows the amount of fabric Camille used based on the number of headbands that she made. Find the slope, and explain what it means in the context of the situation.
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if f(x) = -6x - 2. find f (-3)
Answer:
f(- 3) = 16
Step-by-step explanation:
substitute x = - 3 into f(x) , that is
f(- 3) = - 6(- 3) - 2 = 18 - 2 = 16
An object is dropped from the top of a tower with a height of 1190 feet. Neglecting air resistance, the height of the object at time t seconds is given by the polynomial "-16t^2+1190." Find the height of the object at t=1 second
The height of the object at the time t = 1 second is given by 1174 feet.
Given the height of tower is 1190 feet.
The height of the object at time t seconds is given by,
h(t) = [tex]-16t^2[/tex] + 1190
So the height of the object after time t = 1 second is given by,
h(1) = [tex]-16\times 1^2+1190[/tex] = -16 + 1190 = 1174 feet
Hence the height of the object at the time t = 1 second is 1174 feet.
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Which ordered pair is a solution of the linear equation system
x + 4y = 18 and -3x + 2y = 16?
F. ( -2,-5)
G. (-2, 5)
H. (2, 5)
I. (2, -5)
Answer:
G is correct.
Step-by-step explanation:
[tex] - 2 + 4(5) = - 2 + 20 = 18[/tex]
[tex] - 3( - 2) + 2(5) = 6 + 10 = 16[/tex]
So G (-2, 5) is correct.
There's nothing here
Evaluate the expression if a=−12, b=34, and c=−23.
−||6c−16b||+1
The value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.
We that the modulus always gives a positive quantity.
For example: || -5 || = 5, etc.
We are given;
a = −12, b = 34, and c = −23.
We need to find − || 6c − 16b || + 1.
The solution of an algebraic expression is obtained by substituting the given values in the expression.
Substitute the given value in the above expression, we will get;
− || 6c − 16b || + 1
= − || 6 * -23 − 16 * 34 || + 1
= − || - 138 − 544 || + 1
= − || - 682 || + 1
= − 682 + 1
= - 681
So, the value of − || 6c − 16b || + 1 is - 681.
Thus, the value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.
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-(x - 2) - 2(x - 1) = 8
-(x)-(-2)-2(x)-2(-1)=8
-x+2-2x+2=8
-x-2x+2+2=8
-3x+4=8
-3x=8-4
-3x=4
[tex]\frac{-3x}{-3} =\frac{4}{-3} \\x=-\frac{4}{3}[/tex]
An infant drinks about 26 ounces of milk per day. About how many quarts of milk does the baby drink in 4 weeks?
Answer:
Expert-Verified Answer
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Answer: 19.25 quarts of milk the baby drink in 4 weeks.
We know 1 week = 7 days
So, 4 weeks = 4*7 = 28 days.
In 1 day baby drinks = 22 ounce
In 28 days baby drinks = 28*22 = 616 ounce.
1 quarts = 32 ounces.
So, 616 ounce = 616/32 = 19.25 quarts.
Answer:22.75
Step-by-step explanation: 26 x 7 x 4 = 728 ounces in 4 weeks
theres 32 ounces in a quart
so 728 over 32 will equal 22.75
Draw the given optimization problem and solve it. Find the volume of the largest right circular cylinder (in units3) that fits in a sphere of radius 4 units.
The volume of the largest right cylinder that fits in a sphere of radius 4 units is 143 m².
Let the diameter of the cylinder be “d" and the height of the cylinder be “h".
Given radius of the sphere = r = 4m
Diameter of the sphere = d = 2r = 2×4 = 08 m
As the cylinder is inscribed in the sphere
Therefore, the diameter of the cylinder be “d" is equal to the height of the cylinder be “h".
i.e, d = h
By Pythagoras Theorem, In triangle ABC
AB²+BC²=AC²
Or, d²+h² = (8)²
Or, h²+h² = 64
Or, 2h² = 64
Or, h² = 64/2
Or, h = √32
And d =√32
Or, r = d/2
= √32/2 =16/√32
Or, r = 16/√32
Volume of the cylinder = πr²h
=22/7 × (16/√32 )² × √32
= 22/ 7 × 8 ×√32
= 142.229
Rounding up the value 142.229 in 143 m³
Therefore, the largest volume of the cylinder = 143 m³
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A canoe rental service charges a $20 transportation fee and $30 dollars an hour to
rent a canoe. Write and graph an equation representing the cost, y, of renting a
canoe for × hours.
The equation representing the cost of the canoe rental company is given by y = 30x + 20 .
Let the total cost for renting a canoe be y.
Let the canoe is being rent for x hours.
now the cost for renting the canoe at 30 dollars per hour = 30x
Total cost of renting the canoe = 30x + 20
But the total cost is y.
Hence the equation to represent this situation is given by
y = 30x + 20 which is a straight line of the form y = mx +c, where the slope is 30 and the y-intercept is 20.
Now we will plot the graph for this equation.
At x = 0 , y = 20
At x = 1 , y = 50
At x= -3 , y = -70
Hence the graph of the line passes through these points on the cartesian plane.
The graph of the line is attached below.
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a particular fruit's weights are normally distributed, with a mean of 641 grams and a standard deviation of 23 grams. if you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than how many grams? give your answer to the nearest gram.
If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than 665 grams.
In statistics, mean is the ratio of sum of all the observations and total number of observations in a data set.
How to calculate their mean weight will be greater than how many grams?
Given that from the question
Mean = 641 grams
standard deviation 24 grams
If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?
The formula for the calculating the x value in the normal distribution is,
x = μ + zσ
The level of significance is = 15% = 0.15
Therefore,
z = (=normsinv (1 - α))
= (=normsinv (1-0.15))
= (=normsinv(0.85))
= 1.036
The critical value of z is 1.036
z = 1.036
(x - μ) / σ = 1.036
x = μ + 1.036σ
= 641 + 1.036*23
= 641 + 23.828
= 664.828
= 665grams (rounded to the nearest gram)
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what is the volume of the following rectangular prism? 1 1/3 units 4 1/2 units2
Can you help me because I don’t really understand what do you mean you know I just won the answer it or give me the answer
A painter can paint 175 square feet per hour. She charges $0.54 per square foot. Today she paints for 5.5 hours. How much will she charge?
The amount that the painter will charge is $519.75.
What is the cost?From the information illustrated, the painter can paint 175 square feet per hour and she charges $0.54 per square foot and then paints for 5.5 hours.
The amount that she will charge will be:
= Number of square foot × Amount charged × Number of hours
= 175 × $0.54 × 5.5
= $519.75
The amount is $519.75.
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The shape below is made of two rectangles joined together. 5 cm 9 cm 8 cm 5 cm Find the total area of the shape. Optional working Answer: cm²
Answer:
length × width
5×9=45cm²
45cm²×2=90cm²
Tthe total area of the shape is 85 cm².
How to solve for the areaRectangle 1:
Length = 9 cm
Width = 5 cm
Area of Rectangle 1 = Length * Width
= 9 cm * 5 cm
= 45 cm²
Rectangle 2:
Length = 8 cm
Width = 5 cm
Area of Rectangle 2 = Length * Width = 8 cm * 5 cm = 40 cm²
Total area of the shape
= Area of Rectangle 1 + Area of Rectangle 2 = 45 cm² + 40 cm²
= 85 cm²
Therefore, the total area of the shape is 85 cm².
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