What is the scale factor, without units, of 1 in : 14 ft and 1 in : 30 yard
The scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1: 168 and 1: 1080 respectively.
What is scale factorScale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.
For the ratio 1 in : 14 feet, we convert to the same unit in inches:
1 foot = 12 inches
14 feet = 12 × 14 inches
14 feet = 168 inches
1 in = 168 in
1 : 168
For the ratio 1 in : 30 yards, we convert to the same unit in inches:
1 yard = 36 inches
30 yards = 36 × 30 inches
30 yards = 1080 inches
1 in = 1080 in
1 : 1080
Therefore, the scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1 : 168 and 1 : 1080 respectively.
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The monthly dues for a premium membership at a health club is $15 more than the cost of a standard membership.
The premium membership is $40 per month.
What is the cost of a standard membership?
please explain how you got the answer
Answer:
To find the cost of a standard membership, we need to subtract the $15 premium from the monthly premium membership cost of $40.
$40 - $15 = $25
Therefore, the cost of a standard membership is $25 per month.
in which quadrant is the point ( - 2 , - 3 ) located? A. quadrant iv B. quadrant iii C. quadrant i D. quadrant ii
Since both the coordinates of (-2,-3) are negative the point lies in option B: quadrant iii.
What is a quadrant?
A quadrant is an area or section of a cartesian plane that results from the intersection of two axes. It is used to establish a point's location in a plane.
Consider the point A = (x,y) given in the coordinate system, where x and y are arbitrary numbers.
If x and y are positive numbers then point A is in the first quadrant.
If x is negative number and y is positive then point A is in the second quadrant.
If x and y are negative numbers then point A is in the third quadrant.
If x is positive number and y is negative then point A is in the fourth quadrant.
Now the given point is (-2,-3).
The first coordinate of this point is a negative number, and the second is also negative.
So, the point lies in third quadrant.
Therefore, (-2,-3) is in 3rd quadrant.
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please help i will award brainliest
The given diagram in the image is dilated by a scale factor of 1.5.
What is a scale factor?The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or decrease
The coordinate point of the image is at 2. After dilation, the point will reach the coordinate at 5.
The scale factor of the point will be calculated as:-
Scale factor = 9 / 6
Scale factor = 1.5
Therefore, the scale factor for the given diagram in the image is 1.5.
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The flight time from Boston to London is 6 hours 20 minutes. I arrive London at 4:05pm. What time did I set off from Boston
Answer:
Step-by-step explanation:
4:05pm go back 4hours and it’s 12:05, then go back another 2 hours, 10:05, then go back another 20mins and it’s 9:45am
Suppose you purchased a shirt for $16.51 using a coupon. If the shirt originally costs $25.40, what was the percent discount from the coupon? Simplify your answer completely.
The discount can be found by subtracting the sale price from the original price:
$25.40 - $16.51 = $8.89
So the discount was $8.89.
To find the percent discount, we can divide the discount by the original price and multiply by 100:
$8.89 / $25.40 * 100% = 35%
Therefore, the percent discount from the coupon was 35%.
Eli and Pierre wanted to buy $40 of breakfast rolls for guests. Bagels B are $1.25, and Crossiants C are $2 each. With the extra guests coming, they later increased their budget to $55.
The difference between the vertical intercepts is ________
Answer:
The difference between the vertical intercept is a ratio of 20$ so the difference in intercepts is about 2.50$ or 20 spaces.
Hope this helps
Tallulah wants to buy a car for \$18,500$18,500, but can only get a loan from the bank for \$15,725$15,725. What percentage does Tallulah have to put down in order to pay for the car?
The percentage Tallulah have to put down in order to pay for the car is given by the equation A = 15 %
What is Percentage?A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage Tallulah have to put down in order to pay be A
Now , the equation will be
The price of the car = $ 18,500
The amount of money Tallulah can get from the bank = $ 15,725
So , the remaining amount = price of the car - amount of money Tallulah can get from the bank
Substituting the values in the equation , we get
The remaining amount = 18,500 - 15,725
The remaining amount = $ 2,775
Now , $ 2,775 = A % of price of the car
So , 2,775 = ( A/100 ) x 18,500
On simplifying the equation , we get
Divide by 18,500 on both sides of the equation , we get
A/100 = 0.15
Multiply by 100 on both sides of the equation , we get
A = 15 %
Hence , the percentage is 15 %
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Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
The expression that is not equivalent is 23 + (-27) + 16 + 32. Option C
What is PEDMAS?PEDMAS is described as a mathematical acronym that represents the arithmetic operations in the other of their usage in calculation.
They are;
ParenthesesExponentDivisionMultiplicationAdditionSubtractionFrom the information given, we have that;
23 + ( − 27 ) − 16 − ( − 32 )
expand the parentheses, we get;
23 - 27 - 16 + 32
Add the values
23 - 27 - 16
Now, subtract the values
-20
Hence, the value is -20
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The complete question
Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )
23 - 27 - 16 + 3223 - 27 - 16- (-32)23 + (-27) + 16 + 3223 + (-27) + (-16)- (-32)A researcher interested in the effectiveness of organized diet groups on weight loss weighed five clients after several weeks on the program. The weight-loss scores (in pounds) were as follows: 13 12 6 9 9 10 Calculate the (a) range, (b) inter-quartile range, and (c) variance and standard deviation for these weight-loss scores.
Range = 7. IQR = 4.5. Variance: 8.67, Std Dev: 2.96 when researcher organized diet groups on weight loss weighed five clients after several weeks on the program.
The range of the weight-loss scores can be calculated by subtracting the smallest value from the largest value. In this case, the range would be
13 - 6 = 7.
The inter-quartile range (IQR) is calculated as the difference between the 75th percentile and the 25th percentile of the data.
IQR: 11.25 - 6.75 = 4.5
To calculate the variance, first find the mean weight-loss score by summing all the scores and dividing by the number of clients: (13 + 12 + 6 + 9 + 9 + 10) / 6 = 9.17. Next, subtract the mean from each score and square the result for each client:
[tex](13 - 9.17)^2 = 3.69\\(12 - 9.17)^2 = 1.69\\(6 - 9.17)^2 = 16.0\\(9 - 9.17)^2 = 0.02\\(9 - 9.17)^2 = 0.02\\(10 - 9.17)^2 = 0.69[/tex]
Next, sum the squared deviations and divide by the number of clients minus one (n-1):
(3.69 + 1.69 + 16.0 + 0.02 + 0.02 + 0.69) / (6-1) = 4.83
The variance is 4.83 and the standard deviation is the square root of the variance: [tex]\sqrt{(4.83)} = 2.19.[/tex]
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what is the weight of a 3-pound human brain in ounces
Answer:
The average weight of a 3-pound human brain in ounces is approximately 48 ounces.
Approximate the area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2]
by calculating the sum of the areas of 4 rectangles with…….
The approximate area between the x-axis and the function, f(x) = x² + 3, obtained by finding the sum of the of the four rectangles is Area ≈ 9.75
What is the area between the x-axis and the graph of a function?The area between the x-axis and the graph under a function can be referred to as the area under a curve of the function, which can be found using definite integrals.
The area between the x-axis and the function f(x) = x² + 3 over the interval [0, 2], can be found by finding the area of the rectangular bars, A, in the figure as follows;
The values at the endpoints of the rectangles are; 0.5, 1, 1.5, and 2
Therefore;
f(0.5) = 0.5² + 3 = 3.25
f(1) = 1² + 3 = 4
f(1.5) = 1.5² + 3 = 5.25
f(2) = 2² + 3 = 7
Therefore; A = 0.5 × f(0.5) + 0.5 × f(1) + 0.5 × f(1.5) + 0.5 × f(2)
Plugging in the values of the function, we get;
Area ≈ 0.5 × 3.25 + 0.5 × 4 + 0.5 × 5.25 + 0.5 × 7 = 9.75
The approximate area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2] is about 9.75 square units
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Find the compounded ratio of 2:3 and 9:7.
Answer:
Step-by-step explanation:
Compound ratio of 2:3 and 9:7 is
2x9=18
3x7=21
Answer: 18:21
Have been completely stuck can I get some help on this?
Answer:
1/2x + 6
4
-2x + 5
Step-by-step explanation:
Find the slope (rise over run) and the y intercept for each function.
Is the integer x divisible by 6 ? (1) x + 3 is divisible by 3. (2) x + 3 is an odd number.Answer choices:
(a) Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.
(b) Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.
(c) Either statements are NOT sufficient, but BOTH together are sufficient.
(d) Each statement ALONE is sufficient.
(e) Neither statement Alone is sufficient.
For the statement "Integer x divisible by 6" the option C is correct.
Either statements are NOT sufficient, but BOTH together are sufficient.
What is integer?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
(1) x + 3 is divisible by 3
This means that x is a multiple of 3.
Hence x + 3 is a multiple of 3.
But x could be 0, 3, 6. If x = 3, x is not divisible by 6.
Otherwise it is.
So, this statement is insufficient.
(2) x + 3 is an odd number
This means that x is an even number.
X can be 6, or 10.
So, this statement is insufficient.
Together -
From (1) it is known that x is a multiple of 3.
Hence X can be 0,3,6,9,12,15,18,21,24,27,30.
From (2) it is known that x is even.
Hence X can be 0,6,12,18,24,30.
Therefore, x is divisible by 6.
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Write the solution set of the given homogeneous system in parametric vector form. x1 + 2x2-15x3 = 0 2x1 + x2-15x3-0 X1X2 where the solution set is x = | x2 X3 x=x3 (Type an integer or simplified fraction for each matrix element.
The solution set of the given homogeneous system in parametric vector form is x₁ = 5 = x₂ , x₃ = 1.
What is parametric vector form?
The identity matrix's two columns, which stand in for the two leading coefficients in the row echelon form of the original matrix, are added to create the parametric vector.
We are given set of equations as:
x₁ + 2x₂ - 15x₃ = 0
2x₁ + x₂ - 15x₃ = 0
-x₁ + x₂ = 0
Now, representing this in the matrix form, we get
[tex]\left[\begin{array}{cccc}1&2&-15&0\\2&1&-15&0\\-1&1&0&0\end{array}\right][/tex]
Now, we will reduce the matrix i.e. in row echelon form using elementary operations
From this, we get
[tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&-5&0\\0&0&0&0\end{array}\right][/tex]
So, we get that x₃ is the free variable.
Now, representing this in the parametric vector form, we get
x₁ - 5x₃ = 0
x₂ - 5x₃ = 0
x₃ = x₃
From this, we get
x₁ = 5x₃
x₂ = 5x₃
x₃ = x₃
So, we now get
x = [tex]\left[\begin{array}{c}x_{1} &x_{2} &x_{3} \end{array}\right][/tex]
This is equal to
x = [tex]\left[\begin{array}{c}5x_{3} &5x_{3} &x_{3} \end{array}\right][/tex]
Thus,
x = [tex]\left[\begin{array}{c}5 &5 &1 \end{array}\right][/tex]
Hence, the solution is x₁ = 5 = x₂ , x₃ = 1.
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If h(x) =x+2 , g(x) =x² and f(x) =-x , find the values of x for which gh(x) =f(x)
The values of x for which gh(x) = f(x) are -1 and -4.
As a result, we have gh(x) = g(h(x)) = g(x + 2). ² = x² + 4x + 4 f(x) = -x
The equation must be solved in order to determine the range of x values for which gh(x) = f(x):
x² + 4x + 4 = -x
When all the phrases are moved to the left, we obtain:
x² + 5x + 4 = 0
This quadratic equation has the following factors:
(x + 1)(x + 4) = 0
Thus, either x + 1 = 0 or x + 4 = 0 is the answer.
We obtain x = -1 or x = -4 after solving for x.
Hence, -1 and -4 are the values of x for which gh(x) = f(x).
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A person invested $8, 700 in an account growing at a rate allowing the money to
double every 15 years. How long, to the nearest tenth of a year would it take for the
value of the account to reach $23, 100?
The time it takes for the balance of the account to reach $23,100 is given as follows:
21 years.
How to model the situation?An exponential function is defined as follows:
y = ab^(x/n).
In which the parameters are defined as follows:
a is the initial value.b is the rate of change.n is the time needed for the rate of change.In the context of this problem, the parameter values are given as follows:
a = 8700, b = 2, n = 15.
Hence the function for the balance after x years is given as follows:
y = 8700(2)^(x/15).
Then the time needed for a balance of $23,100 is given as follows:
23100 = 8700(2)^(x/15).
2^(x/15) = 23100/8700
x/15 = log2(23100/8700)
x/15 = 1.41
x = 15 x 1.41
x = 21 years.
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Beau buys a skateboard with a price tag of $82.50. The tax rate is 8%. How much does he pay, including tax?
Enter the correct answer in the box.
$89.1 is the amount paid by Beau to buy skateboard.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Beau buys a skateboard with a price tag of $82.50
The tax rate is 8%
Let us find what 8% of 82.50
Convert 8% to decimal value
8/100=0.08
0.08×82.5=$6.6
Now let us find the amount he paid including tax
$82.50+$6.6
$89.1
Hence, $89.1 is the amount paid by Beau to buy skateboard.
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Are the two triangles similar? If so, state the reason and the similarity statement.
A) Impossible to determine
B) The triangles are not similar.
C) Yes, SSS;VWX ~ YZX
D)Yes, SAS; VWX~YZX
The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The ratio of the corresponding sides are given as,
YX / XV = ZX / XW
3 / 9 = 2 / 8
1 / 3 ≠ 1 / 4
The ratio of the corresponding sides are different. Then the triangles are not similar. Then the correct option is B.
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A train leaves San Diego at 4:00 PM. A second train leaves the same city in the same direction at 6:00 PM. The second train travels 42mph faster than the first. If the second train overtakes the first at 8:00 PM, what is the speed of each of the two trains?
The ratio of cats to dogs is 4:5 if there are 20 dogs how many are there ?
SHOW YOUR WORKG!
Answer: 16 cats
Step-by-step explanation: how many times does 5 go into 20?? 4 times (5x4) so you multiply 4 by 4
Help please! Easy points!
the follow set of data represents orders filled per day, find the sample standard deviation: 5, 13, 9, 10, 5, 12 round your answer to one decimal place.
The Standard deviation of data(5, 13, 9, 10, 5, 12) that represents orders filled per day is 3.4
The sample standard deviation formula looks like this:
s = √Σ(X-x)² / √n-1
Where….
s = sample standard deviation
Σ = sum of…
X = each value
x = sample mean
n = number of values in the sample
We have,
Number of values in the sample, n = 6
sample mean, x = 5+13+9+10+5+2 / 6 = 9
So sample standard deviation, S = √Σ(X-x)² / √n-1
s = √58/√5
s = 7.6/2.2
s = 3.4
Therefore sample standard deviation of data that represents orders filled per day is 3.4
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The non-right angles of a right triangle are in the ratio 1: 5, Write an equation that could be used to find the measure of each angle.
Answer: 6x=90
Step-by-step explanation:
We know that one angle in a right triangle is 90 degrees and the sum of all the angles is 180, so we can start by subtracting 90 from 180. We are left with 90 and now we have angle ratios which represent fractional quantities. We know that one of these quantities is 5 and the other is 1. Their sum is 6 and equals 90. So the proportion would be 6x = 90. The larger angle is 75 degrees and the smaller one is 15.
What is the Mode, Median, Mean and range for the following $32, $87, $67, $32, $32, $87, $77 and $25
Answer:
Mean = $54.875 ($54.88 to nearest cent because $54.875 is impossible)
Median = $32
Mode = $32
Step-by-step explanation:
Mean = all numbers added together / amount of numbers in dataset
$32 + $87 + $67 + $32 + $32 + $87 + $77 + $25 = $439
$439/8= $54.875 = $54.88 to the nearest cent.
Median =
1. Order the numbers. Here's how it's ordered: $25,$32,$32,$32,$67,$77,$87
2. Calculate the middle position with the formula [tex](n+1)/2[/tex] where n is the amount of numbers in dataset (for odd datasets) or find the two middle values (for even datasets.) In this case, it is an odd dataset, so we use the formula.
(7+1)/2 = 4
In the 4th position, the number is $32, so the median is $32.
Mode = The numbers that comes up most often.
In this case, $32 comes up 4 times, which is the most, so the mode is $32.
Brainliest please!
1) Find the perimeter of the composite figure.
A) 23.5
B) 42.9
C) 46.9
D) 31.9
2) Find the area of the composite figure.
A) 64.25
B) 42.95
C) 39.5
D) 103.5
1) The perimeter of the composite figure is 31.9
2) The area of the composite figure is 64.25
What is perimeter?
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.
There are 2 shapes: half circle and right triangle
diameter of half circle ,d=10
radius, r=d/2 = 10/2 = 5
Perimeter of half circle = π r = 3.14 * 5 = 15.7
In the right triangle,
base = 5, line perpendicular to base = 10
hypotenuse² = squares of other 2 sides added
= 5² + 10²
= 25 +100
= 125
hypotenuse = ± √125 = ±11.18
consider positive for length
hypotenuse = 11.18
The perimeter of the composite figure
= Perimeter of half circle +base of right triangle + hypotenuse of right triangle
=15.7 + 5 + 11.18
= 31.9
Area of half circle = 0.5*π *r² = 0.5*3.14*5² = 39.25
Area of right triangle = 0.5*base * height
= 0.5*5*10
= 25
The area of the composite figure
=Area of half circle + Area of right triangle
= 39.25 + 25
= 64.25
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Find the value of Y.
The value of y is 13√2 (optionB)
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
Sin(tetha) = opp/hyp
cos (tetha) = adj/hyp
tan(tetha) = opp/adj
therefore cos 45 = 13/y
1/√2 = 13/y
y = 13√2
therefore the value of y is 13√2
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Answer attached question, show full working and explain what you are doing in each step
Answer:
the required equation is x² -10x +18 = 0
Step-by-step explanation:
Given side x and diagonal 8 cm of a rectangle with perimeter 20 cm, you want to show that the value of x satisfies an equation of the form ...
x² +ax +b = 0 . . . . . where a and b are integers.
PerimeterThe perimeter is the sum of the side lengths. It can be expressed by the formula ...
P = 2(L +W)
Solving for W gives ...
W = P/2 -L
For the given rectangle, the width is ...
W = 20/2 -x = 10 -x
DiagonalThe length of the diagonal is related to the length and width of the rectangle by the Pythagorean theorem.
c² = a² +b²
8² = x² +(10 -x)² = 2x² -20x +100
32 = x² -10x +50 . . . . . . . . divide by 2
x² -10x +18 = 0 . . . . . . . . . . subtract 32
This shows that x must satisfy a quadratic of the form x² +ax +b = 0, where a=-10, and b=18, both integers.
__
Additional comment
The vertex form of the equation is ...
(x -5)² -7 = 0
This has solutions ...
x = 5 ±√7 ≈ {2.354, 7.646} . . . . centimeters
what quantity of 63% chlorine solution must be mixed with a 12% chlorine solution to produce 3876 ml of 15% solution