Therefore, the types of transformation and the value of k for each equation are: Horizontal compression by a factor of 1/2, k = 0. Vertical stretch by a factor of 2, k = 0. Horizontal stretch by a factor of 2, k remains the same as in f(x). Vertical compression by a factor of 1/2, k = 0.
Given by the question.
We can use the given table of values for f(x) and the transformed function g(x) to determine the type of transformation and the value of k for each equation.
g(x) = f(2x):
This is a horizontal compression by a factor of 1/2. The value of k is not affected by this transformation, so k remains the same as in f(x).
g(x) = 2f(x):
This is a vertical stretch by a factor of 2. The value of k is also multiplied by 2, so k = 2(0) = 0.
g(x) = f(1/2x):
This is a horizontal stretch by a factor of 2. The value of k is not affected by this transformation, so k remains the same as in f(x).
g(x) = 1/2 f(x):
This is a vertical compression by a factor of 1/2. The value of k is also divided by 1/2, so k = (0)/(1/2) = 0.
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If there’s two rectangulars that are similar and one is 6cm and 2.8 cm what is the measure of x if the other rectangle is 9cm and x cm
For two similar rectangle value of x is,
⇒ x = 4.2 cm
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
There’s two rectangular that are similar and one is 6cm and 2.8 cm.
Now, By using definition of proportion;
The proportion of there corresponding sides are equal.
Hence, We get;
⇒ 6/2.8 = 9/x
Solve for x;
⇒ x = 9 × 2.8 / 6
⇒ x = 4.2 cm
Therefore, For two similar rectangle value of x is,
⇒ x = 4.2 cm
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a small rug is 1/2 gard wide and 7/6 yards long write and solve an equation to find the area of the rug?
Answer:
Below
Step-by-step explanation:
Area = w X l = 1/2 yd X 7/6 yd = (1*7) / (2*6) = 7/12 yd^2
Answer:
7/12 sq yd
Step-by-step explanation:
The area of a rectangle (which includes a rug) is given by the formula:
Area = Length x Width
We are given that the rug is 1/2 yard wide and 7/6 yards long. So, we can substitute these values into the formula:
Area = (7/6) x (1/2)
To multiply these fractions, we need to find a common denominator. The least common multiple of 6 and 2 is 6, so we can convert both fractions to have a denominator of 6:
Area = (7/6) x (1/2) = (7/6) x (3/3) x (1/2) = 21/36
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:
Area = 21/36 = (21 ÷ 3) / (36 ÷ 3) = 7/12
Therefore, the area of the rug is 7/12 square yards.
The table represents quadratic function g. Which statement is true about the function? -5 -4 -3 -2 -1 0 g (r) -1 O 4. -9 -16 O A. The maximum occurs at the function's x-intercept. O B. The minimum occurs at the function's x-intercept. 0 C. The minimum occurs at the function's y-intercept. D. The maximum occurs at the function's y-intercept.
The correct answer is option D maximum occurs at the function's y-intercept.
What define a quadratic function's essential traits?A quadratic function's graph is a parabola, which, depending on the sign of the coefficient a, might expand upward or downward. A quadratic function's primary traits are:
The greatest or minimum point of the function is at the parabola's vertex.
The vertex serves as the point on the vertical axis of symmetry.
The function's value at x = 0 is known as the y-intercept.
The x-intercepts of the parabola, which appear where the function equals 0, are the roots or zeros of the function.
We must examine the layout of the quadratic function g's graph, which is depicted in the table, in order to ascertain its properties. The chart shows that the parabola's vertex, or maximum/minimum point, is at:
x = -2, where g(-2) = -16.
The y-intercept also happens to be at g(0) = 4.
Hence, the correct answer is option D maximum occurs at the function's y-intercept.
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a motorist covered 90km in the first 1 1/2h and 50km in the next 1/2 find average speed for the second part of the journey
The average speed for the second part of the journey is 100 kilometer per hour.
What is Average Speed?Average Speed is the ratio of the total distance travelled to the total time taken to travel the distance.
Given that,
Distance travelled by motorist in first part = 90 km
Time taken to travel the distance = 1 1/2 hour = 1.5 hours
Distance travelled in second part of the journey = 50 km
Time taken to travel the distance = 1/2 hour = 0.5 hour
Average speed = Distance / Time
= 50 / (1/2)
= 100 km/h
Hence the average speed is 100 kilometer per hour.
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Use the Pythagorean Theorem to find the distance between (0,-4) & (1,5) rounded to the nearest 10th. *
Thus, the separation between the two locations is roughly 9.1 units, rounded to the closest 10.
What is the Pythagoras theorem explained simply?Considering that the hypotenuse is the side that faces the right angle, any right triangle has a works great to the sum of the surfaces of the squares that actually make up its two legs.
According to the Pythagorean Theorem, the square of the hypotenuse, the longest side of a right triangle, is equivalent to the total of the cubes of the other two sides. This theory can be used to determine the separation between the two coordinates (0, -4) and (1, 5), as shown below:
Find the length of the horizontal leg:The two locations are separated horizontally by one unit.
Find the length of the vertical leg:The vertical distance between the two points is 5 - (-4) = 9 units.
Use the Pythagorean Theorem to find the length of the hypotenuse (distance between the points):distance = √((1)² + (9)²)
distance = √(82)
distance ≈ 9.06
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A youth bicycle wheel has a diameter of 20 inches. Darian can reach 3.5 revolutions per second riding down the big hill near his house. What is the approximate linear speed of Darian’s bicycle tire in miles per hour?
The formula for calculating the circumference of a circle (the distance around the circle) is:
C = πd, Where C denotes circumference, d denotes diameter and is a mathematical constant equal to 3.14.
Because the diameter of the bicycle wheel, in this case, is 20 inches, the circumference is:
C = d = 20 inches equals 62.8 inches
Darian covers the following distance per second at 3.5 revolutions per second:
62.8 inches = 220.4 inches distance = 3.5 C = 3.5
To convert this to miles per hour, we need to convert inches per second to miles per hour. Because there are 60 seconds in a minute and 60 minutes in an hour, the following are possible:
An hour has 60 X 60 = 3600 seconds.
There are also 12 inches in a foot and 5280 feet in a mile, so there are:
12 × 5280 = 63360 inches in a mile
Therefore, to convert inches per second to miles per hour, we can use the following conversion factor:
1 inch per second = (3600/63360) miles per hour
Multiplying both sides by the distance in inches per second gives:
distance in miles per hour = (distance in inches per second) × (3600/63360)
Plugging in the values we have calculated, we get:
distance in miles per hour = 220.4 inches per second × (3600/63360)
distance in miles per hour = 12.6 miles per hour (approximately)
Therefore, the approximate linear speed of Darian's bicycle tire is 12.6 miles per hour.
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What is the best estimation of the equation 7 8 − 6 11 ? Drag the numbers into the boxes. Numbers may be used once, twice, or not at all. 1/42011/21/8 − =
For the equation 7/8 - 6/11, the best estimation is obtained as (1) - (1/2) = 1/2
To estimate 7/8 - 6/11, we need to find a common denominator for the two fractions.
One way to do this is to multiply the numerator and denominator of each fraction by the denominator of the other fraction.
So, we have -
(7/8) x (11/11) - (6/11) x (8/8)
= 77/88 - 48/88
= (77 - 48)/88
= 29/88
To simplify this fraction, we can look for common factors in the numerator and denominator.
The fraction 7/8 is almost 1 and the fraction 6/11 is almost 1/2.
Therefore, the best estimation of the equation 7/8 − 6/11 is -
(1) - (1/2) = 1/2
Therefore, the equation is obtained as (1) - (1/2) = 1/2.
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The sum of 4 consecutive integers is -326. Find the largest integer
[tex]x + (x+1) + (x+2) + (x+3) = -326\\[/tex]
[tex]4x + 6 = -326[/tex]
[tex]4x = - 326-6[/tex]
[tex]4x = -332[/tex]
[tex]x = -332/4 \implies x = - 83[/tex]
the integers are:
[tex]-83 < -82 < -81 < -80[/tex]
the largest integer is: -80
find the smallest number, which when is diminished by 7, is divisible by 18,72, and 86.
Answer: 1015
Step-by-step explanation: We will find the factors of all the given numbers by using the prime factorization method. Then we will multiply the factors with the highest degree to find the least common multiple of the given numbers.
Find the value of k such that the line through (7, 1) and (k, 7) is parallel to the line y=3x.
The value of the k is 5
The slope of Parallel lines:The slope of a line is a measure of its steepness or inclination. It tells us how much the line rises or falls as we move horizontally along it.
Parallel lines will have the same slope. That means if two lines are parallel, they have the same steepness or inclination.
Here we have
Equation of the line is y = 3x --- (1)
Equation(1) is in the form y = mx + x
The slope of the line (1) = 3
Let y = m₁x + c is the line that is parallel to line (1)
Since the slope of the parallel lines are equal
=> y = 3x + c --- (2)
Given that the line passes through (7, 1)
=> 1 = 3(7) + c
=> c = - 21 + 1
=> c = - 20
Hence, the equation of the line is y = 3x - 20 --- (3)
It is given that the line will also pass through the point (k, 7)
=> 7 = 3k - 20
=> 3k = 27
=> k = 9
Therefore,
The value of the k is 9
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In a blueprint, each square has a side length of 14
inch.
a. Ceramic tile costs $5 per square foot. How much would it cost to tile the bathroom?
It would cost $
to tile the bathroom.
b. Carpet costs $18 per square yard. How much would it cost to carpet the bedroom and living room?
Step-by-step explanation:
1 blue square on drawing is length 1/4 in but that means 4ft in reality.
so one blue square area correspongs to 4x4 = 16 square feet.
(a) there 6 tiles for the batrhroom = 6x16 sq.ft = 96 sq.ft and the cost will be $480
(b) bedroom + living area = 7x8-8 tiles = 48 tiles = 48 x 16 sq.ft. = 768 sq.ft = 85.33 sq. yards. So the cost will be 85.33*18=$1535.94
(c) unit cost for tile: $5/sq.ft
unit cost for carpet: $1535.94/768sq.ft = $2/sq.ft
The tile has a greater unit cost ($5 per sq.ft) than carpet ($2 per sq.ft)
Tiling the bathroom would cost $25. The price of five squares of tile, or the cost of tiling the bathroom, is: $5 x 5 squares is $25.
How much would it cost to tile the bathroom?a. To calculate the cost of tiling the bathroom, we must first calculate its square footage. Assume the restroom measures 8 feet by 10 feet. We now have the area of:
960 square inches are equal to 8 feet by 12 inches per foot and 10 feet by 12 inches per foot.
The area of the bathroom can be divided by the area of each square, which is 14 inches on the blueprint, to determine the number of squares required:
14 inches by 14 inches divided by 960 square inches equals 4.96 squares.
As we are unable to purchase a fractional quantity of tile, we will round up to 5 squares.
The price of five squares of tile, or the cost of tiling the bathroom, is:
$5 x 5 squares is $25.
Consequently, tiling the bathroom would cost $25.
How much would it cost to carpet the bedroom and living room?b. To calculate the cost of carpeting the bedroom and living room, we must first calculate the square footage of each space. Assume that the living room is 18 feet by 20 feet and the bedroom is 12 feet by 14 feet in size. These areas include:
Bedroom: 168 square feet (12 feet by 14 feet).
The living room is 360 square feet (18 feet by 20 feet).
Divide by 9 to convert square feet to square yards:
Bedroom 168 sq ft / 9 sq ft = 18.67 sq ft
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Determine whether the pair of lines are parallel, perpendicular, or neither.
12x + 4y = 9
12x = 36y + 48
The pair of lines 12x + 4y = 9 and 12x = 36y + 48 are perpendicular.
Determining whether the pair of lines are parallel, perpendicular or neitherFrom the question, we are to determine whether the pair of lines are parallel, perpendicular or neither
To determine whether the pair of lines are parallel, perpendicular, or neither, we need to compare their slopes.
We can rewrite both equations in slope-intercept form, y = mx + b,
Where m is the slope of the line:
12x + 4y = 9
4y = -12x + 9
y = (-3/1)x + 9/4
12x = 36y + 48
12x - 48 = 36y
(1/3)x - 4/3 = y
The slope of the first line is -3/1, and the slope of the second line is 1/3.
Parallel lines have the same slope, so these lines are not parallel.
Perpendicular lines have slopes that are negative reciprocals of each other, meaning their slopes multiply to -1. Therefore, these lines are perpendicular.
Hence, the given pair of lines are perpendicular.
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A recipe for a lemonade punch calls for 6 cups of lemonade for every 24 cups a punch circle the name of the student who wrote an equation that can be used to find X the percentage of lemonade in the recipe
Answer:
Elizabeth
Step-by-step explanation:
Her answer shows the ratio of 6:24- lemonade to punch.
How much would it cost for a customer to purchase 20 subscriptions for each of their 20 employees after a free 30-day trial period, with each subscription costing $10 per month for a yearly commitment? Additionally, they will need 1 extra subscription for a different service for every two employees, with each of these subscriptions costing $5 per month for a yearly commitment. What would be the total cost for the customer for the entire year
The total cost for the customer for the entire year is $48,600.
How to the total cost for the customer for the entire yearThe customer wants to purchase 20 subscriptions for each of their 20 employees, so they need a total of 20 x 20 = 400 subscriptions.
Each subscription costs $10 per month for a yearly commitment,
so the cost for one subscription for a year would be $10 x 12 = $120.
Therefore, the total cost for 400 subscriptions for a year would be $120 x 400 = $48,000.
In addition, they need 1 extra subscription for a different service for every two employees, so they need 20 / 2 = 10 extra subscriptions.
Each extra subscription costs $5 per month for a yearly commitment, so the cost for one extra subscription for a year would be $5 x 12 = $60.
Therefore, the total cost for 10 extra subscriptions for a year would be $60 x 10 = $600.
Adding the cost of the extra subscriptions to the cost of the regular subscriptions, the total cost for the customer for the entire year would be $48,000 + $600 = $48,600.
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Lines m and n are parallel. Which list of angles are all congruent to angle 1?
A. 3, 5, 7
B. 2, 4, 6
C. 4, 5, 6
D. 8, 4, 1
In an examination, Julius scored 5 more marks than John who in turn scored 4 marks less than Grace. If the total mark scored by the three students was 150. Find the mark of each student.
Answer:
Julius: 52
John: 47
Grace: 51
Step-by-step explanation:
Let marks scored by Julius, John and Grace be x, y and z respectively
From the information given,
"Julius scored 5 more marks " → x = y + 5 (1)
"who in turn scored 4 marks less than Grace" → y = z - 4 (2)
Substitute y = z - 4 in equation x = y + 5
→ x = (z-4) + 5
→ x = z - 4 + 5
→ x = z + 1
"The total mark scored by the three students was 150":
x + y + z = 150 (3)
Substitute x = z - 1 and y = z - 4 in equation (3):
← (z + 1) + (z - 4) + z = 150
→ z -+ 1 + z - 4 + z = 150
→ z + z + z + 1 - 4 = 150
→ 3z - 3 = 150
→ 3z = 150 + 3 = 153
→ z = 153/3 = 51
So Grace's mark was 51
John's mark y = z - 4 = 51 - 4 = 47
Julius' mark x = y + 5 = 47 + 5 = 52
Substitute for y from (2) in (4):
2(z - 4) + z = 145
2z - 8 = 145
Find the degree of this polynomial.
8t5 + 5t4
Answer:
5
Step-by-step explanation:
The degree of a polynomial is the highest degree of its terms.
Identify the term with the largest exponent on the variable
Identify the degree of each terms
The degree of 8t5 is 5
The degree of 5t4 is 4
Degree of polynomial = 5
A restaurant offers a 13% discount on all of its food. What is the new total after the discount has
been applied to a bill of £39?
Give your answer in pounds and include the £ sign.
The new total after the 13% discount has been applied to a bill of £39 is £33.93.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To calculate the new total after the discount, we need to first find the amount of discount applied to the original bill.
We can do this by multiplying the original bill by the discount rate (as a decimal):
Discount = 0.13 * £39 = £5.07
Therefore, the amount of the discount is £5.07.
To find the new total, we need to subtract the discount from the original bill:
New total = £39 - £5.07 = £33.93
Therefore, the new total after the 13% discount has been applied to a bill of £39 is £33.93.
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Which of the sets of side lengths below can be used to build a triangle?
1) 5 cm, 3 cm, and 10 cm (2) 4 cm, 12 cm, and 9 cm (3) 5 cm, 2 cm, and 4 cm (4) 3 cm, 5 cm, and 8 cm
Therefore, sets (2), (3), and (4) can be used to build a triangle, while set (1) cannot.
How are triangles determined by length of sides?Any two sides must add up to more than the third side's length in order to form a triangle. Let's use this principle to compare each pair of side lengths:
5 + 3 = 8 + 10 cm, 3 cm, and 5 cm.
3 + 10 = 13 > 5
5 + 10 = 15 > 3
As the total of the lengths of the two shorter sides is not larger than the length of the longest side, a triangle cannot be constructed with this set of side lengths.
3 measurements: 4 cm, 12 cm, and 9 cm 4 + 12 = 16 > 9 4 + 9 = 13 > 12\s12 + 9 = 21 > 4
Given that the total of any two sides is more than the length of the third side, a triangle can be constructed using this set of side lengths.
3, 2, and 5 centimetres
5 + 2 = 7 > 4
2 + 4 = 6 > 5
5 + 4 = 9 > 2
Given that the total of any two sides is more than the length of the third side, a triangle can be constructed using this set of side lengths.
3, 5, and 8 centimetres
3 + 5 = 8 > 8
3 + 8 = 11 > 5
5 + 8 = 13 > 3
Due to the fact that the sum of any two side lengths is bigger, a triangle can be constructed with this combination of side lengths.
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A business sets up a sinking fund so they will have a $61,000.00 to pay for a replacement piece of equipment in 9 years when the current equipment will be sold for scrap. If they make deposits at the end of every 2 months for 9 years in the investment that pays 5.9% compounded every 2 months, what size should each payment be?
The every 2 months payments are $
.
Using compound interest, each payment should be $948.86, rounded to two decimal places.
What is compound interest?The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
[tex]A = P (1 + r/4)^t[/tex]
To determine the size of each payment that needs to be made at the end of every 2 months, we can use the formula for the future value of an annuity:
[tex]FV = Pmt x [(1 + r)^{n - 1}] / r[/tex]
When we enter these values into the formula, we obtain:
In this instance, we know that the sinking fund's future value should be $61,000, the interest rate each 2-month period is 5.9%/6 = 0.983%, and there are a total of 54 periods (9 years x 12 months/year / 2 months/period = 54 periods) in the sinking fund's life.
[tex]$61,000 = Pmt x [(1 + 0.00983)^{54 - 1}] / 0.00983[/tex]
Solving for Pmt, we get:
[tex]Pmt = $61,000 x 0.00983 / [(1 + 0.00983)^{54 - 1}][/tex]
= $61,000 x 0.00983 / 0.6346
= $948.86
Therefore, each payment should be $948.86, rounded to two decimal places.
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What is an equation for the quadratic function represented by the table shown? (table provided below in attachment file)
The quadratic function represented by the table is f(x) = -x² + 4x -1.
What is a quadratic function?A polynomial of degree two in one or more variables is referred to as a quadratic polynomial. The polynomial function that a quadratic polynomial defines is known as a quadratic function.
Here, we have
Given: we have three variables a, b, and c, we can solve this problem by taking three points, say:
(0,-1), (2,3), and (4,-1)
Since we know that the function of the table is a quadratic function, we can start writing this function as follows:
f(x) = ax² + bx + c
So these points must satisfy the equation of the function.
For, (0,-1)
-1 = a(0)² + b(0) + c
c = -1
For, (2,3)
3 = a(2)² + b(2) + c
3 = 4a + 2b -1
4 = 4a + 2b
2 = 2a + b....(1)
For, (4,-1)
-1 = a(4)² + b(4) + c
-1 = 16a + 4b - 1
4a + b = 0...(2)
Now, we have two equations to solve for a and b:
a = -1
b = 4
Now we put the value of a, b, and c in the given equation and we get
f(x) = (-1)x² + 4x + (-1)
f(x) = -x² + 4x -1
Hence, the quadratic function represented by the table is f(x) = -x² + 4x -1.
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A scatter plot is shown on the coordinate plane.
scatter plot with points plotted at 1 comma 7, 1 comma 9, 2 comma 5, 3 comma 6, 3 comma 7, 5 comma 7, 6 comma 5, 7 comma 3, 9 comma 1, and 10 comma 1
Which two points would a line of fit go through to best fit the data?
(3, 6) and (7, 3)
(3, 7) and (9, 1)
(1, 9) and (10, 1)
(1, 7) and (2, 5)
Pοints (1, 9) and (10, 1) wοuld be a line οf fit.
What is a scatter plοt?A scatter plοt is a graph that displays values fοr twο variables as οrdered pairs οf data pοints, with οne variable οn the hοrizοntal axis (x-axis) and the οther variable οn the vertical axis (y-axis).
Tο determine which twο pοints a line οf fit wοuld gο thrοugh tο best fit the data in a scatter plοt, we need tο lοοk fοr the pοints that are clοsest tο the general trend οr directiοn οf the pοints. In this scatter plοt, it appears that the general trend is a dοwnward slοping line.
The twο pοints that wοuld best fit this trend are (1, 9) and (10, 1), which are lοcated at the twο ends οf the scatter plοt and appear tο be the farthest frοm the general trend. Therefοre, the answer is:
(1, 9) and (10, 1)
Hence, pοints (1, 9) and (10, 1) wοuld be a line οf fit.
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A technology salesperson earned $4008 commission on the sale of video equipment. If he earns 6% on all sales, what amount of video equipment did he sell?
Answer: We can start by using the formula for calculating commission:
Commission = Rate x Sales
where Rate is the commission rate and Sales is the amount of sales.
In this case, we know the commission earned ($4008) and the commission rate (6%), but we don't know the amount of sales. We can set up an equation and solve for Sales:
$4008 = 0.06 x Sales
Dividing both sides by 0.06, we get:
Sales = $4008 ÷ 0.06 = $66,800
Therefore, the salesperson sold $66,800 worth of video equipment.
Step-by-step explanation:
drew used these clues to describe a number he wrote.
One digit has a value of 7 x 100,000.
One digit has a value of 9 x 100
One digit has value of 8 x 0.01
Which could be the number Drew wrote?
The number that Drew wrote is 790,800.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented with symbols, such as numerals, and words, such as "three" or "three hundred." Numbers can be used to represent quantities, distances, sizes, and other measurements. In mathematics, number theory is the study of the properties of numbers, such as addition, subtraction, multiplication, and division. Number theory is also used in other sciences, such as physics and computer science.
This is determined by taking the value of each digit and multiplying it by the exponential value that Drew described. The first digit has a value of 7 x 100,000, the second digit has a value of 9 x 100, and the third digit has a value of 8 x 0.01. Therefore, the number is 790,800.
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Given the linear equation y = 2 x + 5 , evaluate y when x = 9 .
Max loves apples. Last week, he bought four pounds and paid $28.
This week he bought only a half of a pound and paid $3.50.
Is the relationship between the pounds of apples and the cost a proportional relationship? ASAP
Answer:
Step-by-step explanation:
yes this relationship is pporportianal
Please help!! Ill give the brainliest thing! :)
Answer: the second one
Step-by-step explanation:
0.2; for each additional day after the kitten is born, its weight is predicted to increase by 0.2 ounces.
Fight
14. Sasha has 2 blocks of clay shaped like the 15.
LEGCM
So hap
rectangular prism below. She joins them to form
a rectangular prism with a length of 12 inches.
What is the surface area of the larger prism?
6 in.
2 in.
2 in.
The surface area of the larger prism is 24b + (5/2)(bc + bd + cd) + 5/2.
What is surface area ?Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.
Let's call the other dimensions of the blocks "a", "b", "c", and "d", with "a" and "c" being the lengths, and "b" and "d" being the widths. Then, we have:
Block 1: a x b x c = 15
Block 2: a x b x d = 15
When we join the blocks together, we get a larger rectangular prism with dimensions 12 x b x (c + d). The surface area of this prism can be found by adding up the areas of its six faces:
Surface area = 2(12b) + 2(bc + bd + cd)
Surface area = 24b + 2(15 + bc + bd + cd)/12
Surface area = 24b + (5/2)(bc + bd + cd) + 5/2
Therefore, the surface area of the larger rectangular prism is given by:
Surface area = 24b + (5/2)(bc + bd + cd) + 5/2
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Note: This question is incomplete so i have given generalized answer
A house is purchased at a price of $340,000. The bank requires a 10% down payment. The current mortgage rate is 5.3%. What is the monthly payment for a 30 year mortgage in this scenario? a $1572 b $1826 c $1699 d $1043
The monthly payment for a 30-year mortgage in this scenario is $1,713.78.
What are Percentages?
Percentages are a way of expressing a proportion or ratio in terms of a fraction of 100.
To solve this problem, we can use the formula for calculating the monthly payment for a mortgage:
[tex]M = P[r(1+r)^n/((1+r)^n)-1][/tex]
where M is the monthly payment, P is the principal (the amount borrowed), r is the monthly interest rate, and n is the number of monthly payments (the term of the loan in months).
First, we need to calculate the down payment, which is 10% of the purchase price:
Down payment = 0.1 x $340,000 = $34,000
The principal is the purchase price minus the down payment:
Principal = $340,000 - $34,000 = $306,000
Next, we need to calculate the monthly interest rate. The annual interest rate is 5.3%, so the monthly interest rate is:
r = 0.053/12 = 0.00441667
Finally, we need to calculate the number of monthly payments. A 30-year mortgage has 360 monthly payments (30 years x 12 months per year).
n = 360
Now we can plug in these values into the formula and solve for M:
[tex]M = \$306,000[0.00441667(1+0.00441667)^360/((1+0.00441667)^360)-1][/tex]
M = $1,713.78
Therefore, the monthly payment for a 30-year mortgage in this scenario is $1,713.78.
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A politician takes an
of 757575 citizens in a county to see what proportion of citizens sampled are satisfied with their standard of living. Suppose that 80\%80%80, percent of the 118{,}000118,000118, comma, 000 citizens in the county are satisfied with their standard of living.
What are the mean and standard deviation of the sampling distribution of the proportion of citizens who are satisfied with their standard of living?
Choose 1 answer:
The mean of the sampling distribution is 606060 and the standard deviation is 871.78.
The central limit theorem is what?As long as the sample size is sufficient (usually, n 30), the central limit theorem implies that if we repeatedly take random samples from a population, the sampling distribution of the sample means will resemble a normal distribution, regardless of the form of the population distribution. This indicates that given the sample mean and standard deviation, we may utilise the normal distribution to draw conclusions about the population mean. Because it enables us to estimate population parameters even when we don't know the population distribution, the central limit theorem is significant.
Given that,
n = 757575
p = 80% = 0.8
q = 1 - 0.8 = 0.2
The mean of the binomial distribution is given as:
Mean: μ = np = (757575)(0.8) = 606060
The standard deviation of the binomial distribution is given as:
σ = √(npq) = √((757575)(0.8)(0.2)) = 871.78
Hence, the mean of the sampling distribution is 606060 and the standard deviation is 871.78.
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