The percent will the fraction decrease should be 80%.
Important information:
In the case when its numerator is decreased by 85% and its denominator is decreased by 25%
Calculation of percentage:
= (100-85) ÷ (100 - 25)
= 15%÷ 75%
= 20%
Now the decrease in percentage should be
= 100% - 20%
= 80%
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The correct answer is 80%
rectangle abcd is dilated by a scale factor of 1/4 to form a’b’c’d’. point t is the center of dilation and lies on segment ab as shown
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The line AB has the following coordinates.
A = (1, 4)
B = (6, 4)
The distance between AB is given as:
AB = √(6 - 1)² + (4 - 4)²
AB = √(5)²
AB = 5
The slope of AB = 0.
For the dilated rectangle the slope remains the same.
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.
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The correct question is:
The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
Tyler collects 1242 cans of pet food. He gives 150 cans to the vet. Then he packs 9 cans in each box to give to the animal shelter. How many cans of pet food are not in a box?
Answer:
121
Step-by-step explanation:
1242-150=1092/9 = 121 (remainder 3)
Answer: 121
Step-by-step explanation: 1241 - 150 / 9
The annual profits for a company are given
in the following table, where x represents
the number of years since 2006, and y
represents the profit in thousands of
dollars. Write the linear regression
equation that represents this set of data,
rounding all coefficients to the nearest
hundredth. Using this equation, estimate
the calendar year in which the profits
would reach 482 thousand dollars.
Years since 2006 (x)
0
1
2
3
4
5
Profits (y)
(in thousands of dollars)
147
167
209
239
250
267
The linear regression of the data is given as follows:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is of:
2019.
How to find the equation of linear regression?To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator.
The points for this problem are given as follows:
(0, 147), (1, 167), (2, 209), (3, 239), (4, 250), (5, 267).
Hence the equation is of:
y = 25.1x + 150.4.
The estimate for the year in which the profit would reach $482,000 is x years after 2006, when y = 482, hence:
482 = 25.1x + 150.4.
x = (482 - 150.4)/25.1
x = 13.
2006 + 13 = 2019 -> year.
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scores turned in by an amateur golfer at the bonita fairways golf course in bonita springs, florida, during and are as follows: 2018 season: 73 77 78 76 74 72 74 76 2019 season: 70 69 74 76 84 79 70 78 a. use the mean (to the nearest whole number) and standard deviation (to decimals) to evaluate the golfer's performance over the two-year period. mean standard deviation mean standard deviation b. what is the primary difference in performance between and ? - select your answer - what improvement, if any, can be seen in the scores? - select your answer -
A) The mean of 2018 scores: μ₂₀₁₈ = 75
The mean of 2019 scores: μ₂₀₁₉ = 75
The standard deviation of 2018 scores: s₂₀₁₈ = 2.07
The standard deviation of 2019 scores: s₂₀₁₉ = 5.26
B) The primary difference is that variation is higher in the 2018 season than the 2019 season.
A)
We know that the mean is nothing but the sum of all scores divided by the number of scores.
Thus the mean for 2018 scores is:
μ₂₀₁₈ = (73 + 77 + 78 + 76 + 74 + 72 +74 + 76)/8
μ₂₀₁₈ = 75
Similarly the mean for 2019 scores is:
μ₂₀₁₉ = (70 + 69 + 74 + 76 + 84 + 79 + 70 + 78)/8
μ₂₀₁₉ = 75
We know that the formula for the standard deviation is:
[tex]s=\sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1} }[/tex]
where s sample standard deviation
n the size of the sample
[tex]x_i[/tex] each value from the sample
[tex]\bar{x}[/tex] the sample mean
Using this formula, the standard deviation for 2018 scores is:
s₂₀₁₈ = [tex]\frac{\sqrt{ (73-75)^2 + (77-75)^2 + (78-75)^2 + (76-75)^2 + (74-75)^2 + (72-75)^2 +(74-75)^2 + (76-75)^2} }{7}[/tex]
s₂₀₁₈ = 2.07
And the standard deviation for 2019 scores is:
s₂₀₁₉ = [tex]\frac{\sqrt{ (70-75)^2 + (69-75)^2 + (74-75)^2 + (76-75)^2 + (84-75)^2 + (79-75)^2 +(70-75)^2 + (78-75)^2} }{7}[/tex]
s₂₀₁₉ = 5.26
B)
We cwn observe that both the two years have the same mean but the 2019 scores have higher variation as compared to 2018 scores.
Thus, the variation in scores was higher in 2019.
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Find the complete question below.
which function represents an exponential decay function with a y-intercept of -3?
a. f(x) = (0.5)^x - 4
b. f(x) = (0.5)^x - 3
c. f(x) = 2^x - 4
d. f(x) = 2^x - 3
Answer:
A
Step-by-step explanation:
The line has a negative slope, with a y-intercept of (0,-3), and an x-intercept of (-2,0)
Find the output, y, when the input, a, is 7
Answer: Y would be 4
If you look at the graph and find 7 on the x axis where the inputs are, you can see that if you go up, the only output for 7 is 4.
Chloe borrows 800 from the bank for 3 years at simple interest. The interest she is charged after 3 years is 168. Calculate the rate of simple interest charged at this bank. Give the answer as a percentage
After 3 years the rate of simple interest charged at this to Chloe bank is 7%
We can start by using the formula for simple interest:
Simple Interest = Principal * Rate * Time
where the principal is the amount borrowed, the rate is the interest rate as a decimal, and the time is the duration of the loan in years.
Plugging in the given values, we get:
168 = 800 * Rate * 3
Solving for the rate, we get:
Rate = 168 / (800 * 3) = 0.07
Hence,
The rate of simple interest charged at this bank is 0.07, or 7% as a percentage.
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Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
F) (x, y ) → (2x, 2y)
G) (x, y ) → (1. 5x, 1. 5y)
H) (x, y ) → (3x, 3y)
J) (x, y ) → (4x, 4y)
The best way to represents the change in the vertices of rectangle ABCD to rectangle A'B'C'D' in the attached graph is given by :
option A. (x, y ) → (2x, 2y).
From the attached graph we have,
Coordinates of rectangle ABCD are :
Coordinate of vertex A ( -3, -2 )
Coordinate of vertex B ( -3, 2 )
Coordinate of vertex C ( 3, 2 )
Coordinate of vertex D ( 3, -2 )
And coordinates of A'B'C'D' are:
Coordinate of vertex A' ( -6, -4 )
Coordinate of vertex B' ( -6, 4 )
Coordinate of vertex C' ( 6, 4 )
Coordinate of vertex D' ( 6, -4 )
Coordinate of rectangle ABCD gets dilated by the scale factor of :
Scale factor of 'x' coordinate = -6 / -3
= 2
Scale factor of 'y' coordinate = -4 / -2
= 2
Change in the vertices of rectangle ABCD to A'B'C'D' is given by :
( x , y ) → ( 2x , 2y )
Therefore, the vertices of rectangle ABCD changed to A'B'C'D' is equal to option A. ( x , y ) → ( 2x , 2y ).
The above question is incomplete, the complete question is:
Which best represents the change in the vertices of rectangle ABCD to form rectangle A'B'C'D'?
A) (x, y ) → (2x, 2y)
B) (x, y ) → (1. 5x, 1. 5y)
C) (x, y ) → (3x, 3y)
D) (x, y ) → (4x, 4y)
Graph is attached.
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Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The two triangles in this problem are similar, with the bisection, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
The relationship can be simplified as follows:
x/45 = 0.9.
Applying cross multiplication, the value of x is obtained as follows:
x = 45 x 0.9
x = 40.5.
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I need help…………………………….
a) The Equation is 7.65x + 50 = 149.45.
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours then the amount will be $471.12
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given that;
Members of a car sharing program pay a fee of $50 per month plus $7.65 for every hour they use a car.
And, a members bill was $149.45 last month.
a) Let number of hours for the customer use a car last month = x
So, 7.65x + 50 = 149.45
7.65x = 149.45 - 50
7.65x = 99.45
x = 13
b) The customer used the car for 13 hours.
c) If the car used for 2 days i.e., 48 hours
= 7.65x + 50
= 7.65(48)+ 50
= 471.2
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What is the solution set to the inequality w+ 4<4 (w - 2)?
Select a ray. Move the point on the ray to the correct place on the number line.
-7 -6 -5 -4
H
->
(-)
-3 -2 -1
0 1 2
--
31
3
4 5 6 7
--
+
The solution set to the inequality is w > 3
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
w+ 4<4 (w - 2)
Open the bracket
So, we have the following representation
w+ 4 < 4w - 8
Evaluate the like terms
So, we have the following representation
12 < 3w
Divide by 3
4 < w
So, we have
w > 4
See attachment for number line
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Two joggers run 8 miles and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile they must travel to return to their starting position?
Answer:
A. 9.4 mi
Step-by-step explanation:
Sketch a right triangle with legs of 8 and 5. Shortest distance back to the starting point is the hypotenuse (h) of the triangle:
h² = 8² + 5² = 89
h = √89 = 9.43 mi
Trigonometry question
The value of sin (θ/2) in the trigonometry is π/9
How to find sin (theta / 2)Information given in the problem
tan θ = 7/8,
where
0 < θ < π/2
solving for θ, from tan θ = 7/8
tan θ = 7/8
θ = arc tan (7/8)
θ = 0.7188 radians
soling for sin (θ/2)
= sin (θ/2)
= sin (0.7188/2)
= 0.3517 approximately π / 9
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A 13-ft by 27-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 384 ft^2, how wide is the walkway?
Answer:
w = 25 / 4 feet wide.
Step-by-step explanation:
Let's call the width of the walkway "w."
The area of the rectangular pool is 13 * 27 = 351 ft^2.
The area of the walkway can be calculated by adding up the area of four rectangles, one around each side of the pool:
2 * (13 + w) * w + 2 * (27 + w) * w = 384
Expanding the equation:
2 * 13w + 2w^2 + 2 * 27w + 2w^2 = 384
Combining like terms:
2w^2 + 40w = 384
Solving for w^2:
2w^2 + 40w - 384 = 0
Using the quadratic formula:
w = (-40 ± √(40^2 - 4 * 2 * -384)) / (2 * 2)
Simplifying:
w = (-40 ± √(1600 + 3072)) / 4
w = (-40 ± √4272) / 4
w = (-40 ± 65) / 4
w = (25 / 4) or (-105 / 4)
Since w must be a positive value, w = 25 / 4 feet wide.
Answer:look it up frfr
Step-by-step explanation:
if y x 3 equals to 3/5 y
Answer:
since y = 0 when x = 0
Step-by-step explanation:
We can start by solving for y in the equation:
y * x = 3/5 y
Dividing both sides by y:
x = 3/5
So the equation y * x = 3/5 y can be simplified to:
y = 5/3 x
This equation shows that there is a proportional relationship between y and x, where y is always equal to 5/3 times x. This relationship can be represented on a graph by plotting points (x, y) and drawing a line through them. The slope of the line will be 5/3, and the y-intercept will be 0, since y = 0 when x = 0.
Answer:
y = ±1/√5
Step-by-step explanation:
3y = 3/5y
⇒3y×5y = 3
⇒15y² = 3
⇒y² = 3/15
⇒y² = 1/5
⇒y = ±1/√5
What is the positive solution to the equation 0= 1/4x^2-4
answers;
4
1
-1
-4
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} - 4 = 0[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{1}{4} {x}^{2} = 4[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} = 4 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \sqrt{4 \times 4} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = \pm4[/tex]
[ but since we have been asked for positive solution, it will be 4 ]
Hence, the correct choice is : A.) 4
3. a computer password consists of two lowercase letters followed by a capital letter and four digits. find the total number of possible passwords.
The total number of possible passwords is 17,576,000.
There are several steps involved in calculating the total number of possible passwords.
Step 1: Determine the number of possible choices for the first lowercase letter. Since there are 26 letters in the alphabet, and the password consists of lowercase letters, there are 26 choices for the first letter.
Step 2: Determine the number of possible choices for the second lowercase letter. Since there are 26 letters in the alphabet and repetition is allowed, there are 26 choices for the second letter.
Step 3: Determine the number of possible choices for the capital letter. Since the password requires a capital letter, there are 26 choices for this position.
Step 4: Determine the number of possible choices for the first digit. Since there are 10 digits (0-9), there are 10 choices for the first digit.
Step 5: Determine the number of possible choices for the second digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the second digit.
Step 6: Determine the number of possible choices for the third digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the third digit.
Step 7: Determine the number of possible choices for the fourth digit. Since there are 10 digits (0-9) and repetition is allowed, there are 10 choices for the fourth digit.
Step 8: Multiply the number of choices for each position together to get the total number of possible passwords.
Using the multiplication rule of counting, we get:
Total number of possible passwords = (Number of choices for the first lowercase letter) x (Number of choices for the second lowercase letter) x (Number of choices for the capital letter) x (Number of choices for the first digit) x (Number of choices for the second digit) x (Number of choices for the third digit) x (Number of choices for the fourth digit)
Total number of possible passwords = 26 x 26 x 26 x 10 x 10 x 10 x 10
Total number of possible passwords = 17,576,000
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Consider the original coordinates of the vertices of a parallelogram.
A (-2, 4)
B (4,4)
C (2,-2)
D(-4,-2)
According to the information, the area of the parallelogram plotted from the points would be: 36 cm²
How to find the area of the parallelogram?To find the area of the parallelogram we must divide the parallelogram into a quadrilateral section and another triangular section and find the area of these segments.
According to the above, we can infer that the area of the quadrilateral zone would be
a = b*ha = 4*6a = 24On the other hand, the area of the triangular section would be:
a = b*h/2a = 2 * 6 / 2a = 12 / 2a = 6Additionally, we must multiply the area of the triangular segment by two because there are two triangular sections in the parallelogram. Finally we have to add the area of the quadrilateral and triangle segments to get the total area.
6 * 2 = 1212 + 24 = 36Note: This question is incomplete. Here is the complete information:
TASK
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Dorthy surveyed the first 20 people to use a new website is this s biased or a random sample
It is a biased sample.
What is meant by a random sample?
Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
A random sample is one in which each individual, thing, or event has an equal chance of being chosen. Compared to other types of samples, a random sample has a higher likelihood of being representative of the total population. A skewed sample is one that does not fairly represent the population as a whole.
Here Dorthy considered only the first 20 people and not the whole population so this is not a random sample and it is a biased sample.
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Sarah competes in a long jump competition. Her first jump is 4.25m. Her best jump is 12% more than this. However, her best jump is 15% lower than the winning jump. Work out the length of the winning jump.
Answer:
5.51mStep-by-step explanation:
Let's call the length of the winning jump "w".
Sarah's best jump is 12% more than her first jump, which was 4.25m. So her best jump was 4.25m * 1.12 = 4.77m.
However, her best jump is 15% lower than the winning jump, so we can set up an equation to solve for w:
4.77m * 1.15 = w
Solving for w:
w = 4.77m * 1.15 = 5.51m
So the winning jump was 5.51m.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
Suppose that the amount of algae in a pond doubles every 5 hours. If the pond initially contains
10 pounds of algae, how much algae will be in the pond after 20 hours?
Answer:
160 pounds of algae
Step-by-step explanation:
10 times 2 is 20 ( first 5 hours )
20 times 2 is 40 (10 hours)
40 times 2 is 80 (15 hours)
80 times 2 is 160 ( 20 hours)
there would be 160 pounds of algae
ABCD is a rectangle with sides 8cm and 6cm PQRS is a rhombus
obtained by joining the midpoints of the sides of the rectangle. find
a)The lengths of the diagonals of PQRS?
b)The area of PQRS?
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
What is the area?Surface area refers to the area of an open surface or the border of a multi-object, whereas the area of a plane region or plane field refers to the area of a form or planar material.
The diagonals of the rhombus will be the same as the dimension of the rectangle that is 8 cm and 6 cm.
Then the area of the rhombus is given as,
A = (Product of diagonal of rhombus) / 2
A = (8 x 6) / 2
A = 48 / 2
A = 24 square centimeters
The lengths of the diagonals of PQRS will be 8 cm and 6 cm. Then the area of the rhombus PQRS will be 24 square cm.
The diagram is shown below.
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what are 3 ways to solve 26x14
Answer:
i think this the answer
Step-by-step explanation:
26×14=ans
20×14+6×14=the same answer
10×26+4×26=same answer
2. How many solutions does the system of equations have? (A no solution B exactly one solution c exactly two solutions D infinitely many solutions
The number of solutions of the system of equations is given as follows:
D. Infinitely many solutions.
How to obtain the number of solutions of the system of equations?The system of equations is defined as follows:
4x - 9y = 1.12x - 27y = 3.The second equation was obtained multiplying the first equation by 3, meaning that the two equations are multiples, and thus the system of equations has an infinity number of solutions and the correct option is given by option D.
Missing InformationThe system of equations is defined as follows:
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Suppose your home is located at (0, 0) on a coordinate plane. The school is located 5 miles west of your home. The playground is 3 miles south of the school. What is the shortest distance, in miles, between your home and the playground? Round your answer to the nearest tenth
The shortest distance is 5.83 miles as we calculate this by distance formula.
A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:
PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
The school is located 5 miles west of your home the co ordinate is (-5,0)
The playground is 3 miles south of the school so co - ordinate is (0,-3)
shortest distance = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])
√([tex]5^{2} +3^{2}[/tex]) = √34
=5.830 miles
And this Question also can be do by right angle triangle method
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I need to find the value of x and it's a horizontal line or whatever the cross over like a x (3x-3)°147°
given the set [1,2,3,5,8,13,21,34,55}, how many integers between 3 and 89 cannot be written as the sum of excatly two elements of the set?
The final count of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set is 39.
To determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set {1, 2, 3, 5, 8, 13, 21, 34, 55}, we can use a process of elimination.
First, we can list all the possible sums of two distinct elements of the set. This gives us a total of 28 sums.
Next, we can identify all the integers between 3 and 89 that can be expressed as the sum of two distinct elements of the set. We can do this by checking each integer between 3 and 89 to see if it can be written as a sum of two elements of the set. If an integer can be written as a sum of two elements of the set, we can cross it off the list.
After eliminating all the integers that can be written as a sum of two elements of the set, we are left with the integers that cannot be expressed as such.
In summary, we can determine the number of integers between 3 and 89 that cannot be written as the sum of exactly two elements of the set by listing all possible sums, identifying the integers that can be expressed as such sums, and eliminating them from the list.
The remaining integers are those that cannot be expressed as the sum of exactly two elements of the set.
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suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41 . using the empirical rule, what percentage of the students have grade point averages that are between 1.38 and 3.84 ?
By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.
Here, μ = 2.61 , σ = 0.41
Using the empirical rule :
The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.
2.61 − 0.41 = 2.2
2.61 + 0.41 = 3.02
The range of numbers is 2.2 to 3.02
The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.
2.61 − 2(0.41) = 1.79
2.61 + 2(0.41) = 3.43
The range of numbers is 1.79 to 3.43
Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.
2.61 − 3(0.41) = 1.38
2.61+3(0.41) = 3.84
The range of numbers is 1.38 to 3.84.
Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.
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If 4 is added to twice the number n, the result is the same as if n were increased by 7. What is the value of n?
Answer:
n = 3
Step-by-step explanation:
Starting equation:
2n + 4 = n + 7
Subtract by n on both sides:
n + 4 = 7
Subtract 4 on both sides
n = 3
Check to see if the answer works:
2(3) + 4 = 3 + 7
6 + 4 = 3 + 7
10 = 10
The solution works
n = 3
