Answer:
The expression 4 in x + in 3 - in x can be simplified using logarithmic rules: 4 in x + in 3 - in x = in x^4 + in 3 - in x = in (x^4 * 3 / x) = in (3x^3) Therefore, the expression is equivalent to in (3x^3).
Rachel cycled a total distance of 59,136ft on a bicycle path surrounding a lake. She cycled 4 laps, where each lap was the same length. What was the length of each lap around the lake? Write your answer in miles.
Rachel cycled each lap around the lake that was 2.8 miles long.
What is unit rate?
A unit rate is a ratio in which the denominator is 1. It is a rate that compares a quantity to one unit of another quantity.
First, we need to convert the total distance cycled from feet to miles since the length of each lap is likely to be expressed in miles.
1 mile = 5280 feet
Therefore,
59,136 ft ÷ 5280 ft/mile = 11.2 miles
So, Rachel cycled a total of 11.2 miles around the lake.
Since she cycled 4 laps of the same distance, we can divide the total distance by 4 to get the length of each lap:
11.2 miles ÷ 4 = 2.8 miles per lap
Therefore, Rachel cycled each lap around the lake that was 2.8 miles long.
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The federal government has developed the body mass index (bmi) to determine ideal weights. a person's bmi is directly proportional to his or her weight in pounds and inversely proportional to the square of his or her height in inches. (a bmi of 19 to 25 corresponds to a healthy weight.) a 6-foot-tall person weighing 177 lb has bmi 24. find the bmi (to the nearest whole number) of a person whose weight is 176 lb and whose height is 77 in.
The BMI of a person whose weight is 176 lb and whose height is 77 inches is 21.
First, let's use the given information to find the constant of proportionality in the BMI formula:
BMI = k × (weight in pounds) / (height in inches)²
When the 6-foot-tall person weighing 177 lb has a BMI of 24, we can plug in the values and solve for k:
24 = k ₓ 177 / (72²)
k = 24 ₓ (72²) / 177
k ≈ 9.94
Now we can use this value of k to find the BMI of the person whose weight is 176 lb and whose height is 77 in:
BMI ≈ 21
BMI = 9.94 ₓ 176 / (77²)
Therefore, the BMI (to the nearest whole number) of the person is 21, which falls within the healthy weight range of 19 to 25.
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Anton surveys 80 students at his school and finds that 55% of them have mobile phones. He also finds that 98% of 50% adults have mobile phones. How many more adults than students ?
Answer:
13
Step-by-step explanation:
Student: 80 * 55% = 44
Adult: 50 * 98% = 49
49-44=5
Write 4 as a logarithm with a base 4
Answer: Algebra Examples
Logarithm base 4 of 4 is 1.
Step-by-step explanation:
unity
The value of log 4 to the base 4 is equal to unity. The Antilogarithm of the logarithmic value of 4 is equal to 4.
y = y₁ = m(x − x₁)
Show your work in the space provided below.
1. Find the equation of the line that has a slope of -4 and passes through the point (-3, 7).
Show your work below:
2. Find the equation of the line that passes through the points (4, -3) and (8,9).
Show your work below:
Answer:
see below
Step-by-step explanation:
The equation y - y₁ = m(x − x₁)
1. y - 7 = -4(x - -3)
y - 7 = -4(x + 3)
y = -4x - 12 + 7
y = -4x - 5
2. y - y₁ = m(x − x₁)
9 - -3 = m(8 - 4)
12 = 4m
m = 12/4 = 3
y = mx + b
-3 = 3(4) + b
b = - 3 - 12
b = -15
y = 3x - 15
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 5 units down. A′(−4, −2), B′(4, −2), C′(0, 2) A′(1, −7), B′(9, −7), C′(5, −3) A′(1, 3), B′(9, 3), C′(5, 7) A′(6, −2), B′(14, −2), C′(10, 2)
if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
The x and y coordinates of each of a triangle's vertices must be added to or subtracted from to translate the triangle on a coordinate plane.
Triangle ABC must be translated five units lower in this situation. Thus, we must deduct 5 from the y coordinates of each of its vertices.
A(1, -2) changes to A' (1, -7) B(9, -2) changes to B' (9, -7) C(5, 2) changes to C' (5, -3)
As a result, if triangle ABC is translated 5 units down, the image's coordinates are A′(1, 7), B′(9, 7), and C′(5, 3).
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8a = -12 + 2a me need helpppppppppppppp
Answer: a = -2
Step-by-step explanation:
8a = -12 + 2a
8a - 2a = -12
6a = -12
a = -12/6
a = -2
Twenty four blood samples were selected by taking every seventh blood sample from racks holding 199 blood samples from the morning draw at a medical center
A)calculate the FPCF for this sample
B)Should the population be considered effectively infinite
DO BOTH A AND B URGENT
A) The FPCF for this sample is 0.899. B) The sample size is about 12% of the population size, which is relatively large.
A) The FPCF (Finite Population Correction Factor) is used to adjust for the impact of a finite population on the sampling distribution. The formula for the FPCF is:
FPCF = [tex]\sqrt{((N-n)/(N-1))}[/tex]
where N: size of the population and n: size of the sample.
In this case, the population size is N = 199, and the sample size is n = 24. Therefore, the FPCF can be calculated as follows:
FPCF = [tex]\sqrt{((199-24)/(199-1))}[/tex] = 0.899
So, the FPCF for this sample is 0.899.
B) In general, a population can be considered effectively infinite when the sample size is no more than 5-10% of the population size. In this case, the sample size is n = 24, and the population size is N = 199. Therefore, the sample size is about 12% of the population size, which is relatively large.
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5)
Given:
Prove:
41 and 22 are complementary.
41 = 23
22= 24
23 and 24 are complementary.
2
3
4
[tex] \angle3 \: and \: \angle4 [/tex] are complementary.
What is Complementary angle?
If sum of two angles is 90° then we can say that those angles are complementary.
For example, if [tex] \angle \: a + \angle \: b = {90}^{o} [/tex] then angle a and angle b are complementary.
Here are some examples of complementary angles:
30 degrees and 60 degrees45 degrees and 45 degrees20 degrees and 70 degrees15 degrees and 75 degrees10 degrees and 80 degrees35 degrees and 55 degrees25 degrees and 65 degrees40 degrees and 50 degrees5 degrees and 85 degrees12 degrees and 78 degrees.Here given,
[tex] \angle1 \: and \angle2[/tex] are complimentary.
So,
[tex] \angle1 + \angle2 = {90}^{o} [/tex]
It is clear that [tex] \angle1, \angle2, \angle3, \angle4[/tex] are making a straight angle.
So, we can write,
[tex] \angle1 + \angle2 + \angle3 + \angle4 = {180}^{o} \\ {90}^{o} + \angle3 + \angle4 = {180}^{o} \\ \angle3 + \angle4 = {180}^{o} - {90}^{o} \\ \angle3 + \angle4 = {90}^{o} [/tex]
Here sum of angle 3 and angle 4 is 90°.
According to definition angle 3 and angle 4 are complimentary angles.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
The equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
What is a rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°).
A rectangle has equal and parallel opposite sides.
A rectangle has two dimensions—length and width—because it is a two-dimensional form.
The rectangle's longer side is its length, while its shorter side is its breadth.
So, the area formula of the rectangle:
750 = l * w
750 = x * (x-5)
750 = x² - 5x
x² - 5x - 750 = 0
Equations in the options that are similar:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
Therefore, the equations that can be used to solve for y in the given situation are:
(A) y(y + 5) = 750
(B) y² – 5y = 750
(D) y(y – 5) + 750 = 0
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Correct question:
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options.
NEED ASAP
Answer choices:
a. y(y + 5) = 750
b. y2 – 5y = 750
c. 750 – y(y – 5) = 0
d. y(y – 5) + 750 = 0
e. (y + 25)(y – 30) = 0
Solve the systems by elimination.
x -y = 11
5x + 6y = -44
Answer: (6,-5)
Step-by-step explanation:
Andy has -$45 in his checking account at the beginning of the week. At the end of the week he was paid $30 for moving the grass and $25 for vacuuming the house. How much money does Andy now have in his checking account?
Answer:
we need to add the money Andy earned to the negative balance he had. So, we have:
-$45 + $30 + $25 = $10
Therefore, Andy now has $10 in his checking account.
Answer:
Andy now has $10 in his checking account.
Step-by-step explanation:
Andy starts the week with -$45 in his checking account. When he gets paid $30 for mowing the grass and $25 for vacuuming the house, his total earnings for the week are:
$30 + $25 = $55
To find out how much money he now has in his checking account, we need to add his earnings to his starting balance of -$45. Adding a negative number is the same as subtracting a positive number, so we can write this as:
-$45 + $55 = $10
Therefore, Andy now has $10 in his checking account.
PLS HELP ASP!!!
The state of Colorado is 4 centimeters long and 2 centimeters wide on a map. A cartographer wants to use a scale factor of 3.5 to enlarge the map. What is the area of the enlarged map?
98 cm2
42 cm2
28 cm2
8 cm2
Answer: 98 cm²
Step-by-step explanation:
When a cartographer enlarges a map with a scale factor, both the length and the width are multiplied by the scale factor. In this case, the scale factor is 3.5.
Original dimensions of Colorado on the map:
Length: 4 cm
Width: 2 cm
Enlarged dimensions using the scale factor of 3.5:
Length: 4 cm × 3.5 = 14 cm
Width: 2 cm × 3.5 = 7 cm
To find the area of the enlarged map, multiply the enlarged length and width:
Area = Length × Width
Area = 14 cm × 7 cm
Area = 98 cm²
The area of the enlarged map is 98 cm².
Solve the equation for y in terms of x, and replace y with function notation f(x). Then find f(2).
y+3x^2=5
f(x)=?
f(2)=?
Answer:
[tex]f(x)=-3x^2+5[/tex]
[tex]f(2) = -7[/tex]
Step-by-step explanation:
Given equation:
[tex]y+3x^2=5[/tex]
To solve the equation for y in terms of x, simply subtract 3x² from both sides of the equation:
[tex]\implies y+3x^2-3x^2=5-3x^2[/tex]
[tex]\implies y=-3x^2+5[/tex]
Replace y with the function notation f(x):
[tex]f(x)=-3x^2+5[/tex]
Finally, to find the value of f(2), substitute x = 2 into the function:
[tex]\begin{aligned}\implies f(2)&=-3(2)^2+5\\&=-3(4)+5\\&=-12+5\\&=-7\end{aligned}[/tex]
Answer:
[tex]f(2) = - 7[/tex][tex] f(x) = 5 - 3x^2[/tex]Step-by-step explanation:
To find:-
The value of [tex]f(2)[/tex]Answer:-
We are here a given a equation, with some steps to follow, in order to find out the value of [tex]f(2)[/tex].
Step 1 :- Solve the equation in terms of y ,
The given equation to us is,
[tex]\longrightarrow y + 3x^2 = 5\\[/tex]
To solve for y , we need to transpose 3x² from LHS to RHS , by doing this , the sign changes from positive to neagative .
[tex]\longrightarrow y = 5 - 3x^2 \\[/tex]
Step 2 :- Replace y with function notation [tex]f(x)[/tex]
Just simply replace y here with f(x) as ,
[tex]\longrightarrow f(x) = 5 - 3x^2\\[/tex]
Step 3 :- Find f(2) .
To calculate the value of f(2) , we need to put x = 2 , in the above equation as ,
[tex]\longrightarrow f(2) = 5 - 3(2)^2\\[/tex]
Simplify,
[tex]\longrightarrow f(2) = 5 - 3(4)\\[/tex]
[tex]\longrightarrow f(2) = 5 - 12\\[/tex]
[tex]\longrightarrow \boxed{ \boldsymbol{f(2) = -7 }} \\[/tex]
Hence the required answer is -7 .
Identify the shapes that make up the figure at the left. Then find the perimeter and area of the figure to the nearest hundredth.
Rectangle, semi circle, semi circle
Perimeter: 60.8
Area: 64.2
What is perimeter and area?In mathematics, the two key characteristics of two-dimensional forms are area and perimeter. The difference between area and perimeter is how much room each type of shape takes up.
Mathematical concepts like area and perimeter are crucial because they are applied to daily living. Any size and form, whether regular or irregular, can use this. Each design has a unique area and perimeter calculation. Forms like triangles, squares, rectangles, circles, spheres, etc. should be known to you. Here, the boundaries and surfaces of all forms are explained.
perimeter= 60.8
each of the three shapes' perimeters separately, then sum them all up to get 60.8.
area= 64.2
Calculate the area of each of the three shapes separately, then sum them all up to get 64.2.
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The complete question attached below,
The required size and perimeter of the Area are respectively 27.42 and 64.26 square units.
What is Perimeter of the shape?A shape's perimeter is its circumference. How are perimeters determined? By adding the lengths of each side of a shape, the border may be obtained.
A shape comprised of two circles and a rectangle has been provided.
the size of a circle = 12 - 6 = 6
then radius = 3 units
Perimeter = 3+3+3+3+3+3+π(3)
= 18 + 3.14(3)
= 18 + 9.42
= 27.42 units
and
Area = area of rectangle + area of two half circles
= 12(3) + π(3)²
= 36 + 28.26
= 64.26 sq units.
Therefore, the shape's needed area and perimeter are respectively 27.42 and 64.26 square units.
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Simplify -4x(1-3)-2x+2)
Answer:
The answer is 6x + 2
Step-by-step explanation
I did all the work and I passed on this test so i know this is the answer.
4 1/5 -5/3 subtract
how do i do this eqation
Answer:
38/15
Step-by-step explanation:
4 1/5 - 5/3
4 1/5 = 21/5
21/5 - 5/3 = 63/15 - 25/15 = 38/15
So, the answer is 38/15
The polynomial of degree 4, P(x) , has a root of multiplicity 2 at x=3 and a root of multiplicity 1 at x=0 and x=-1. it goes through point (5,12).
Write the following series in sigma notation. 8+18+28+38+48
Answer:
in the image
Step-by-step explanation:
using the arithmetic formula
a = ao + d(n-1)
we can find the sum of this formula added up 5 times
Please help meeee
describe an incident that shows how you were doing "selection" during the process of perception. Then, give your own example about a stereotype that you do.
The description of the incident is shown below
Describing the incidentOne incident that shows how selection works in the process of perception is when you are at a party and you hear your name being mentioned in a conversation across the room. In this situation, your attention is immediately drawn to the conversation, and you focus on it while filtering out other sounds and distractions around you.
This is an example of selective attention, where you choose to focus on a particular stimulus and ignore others.
As for an example of a stereotype that I have, it is that all people who live in a certain region or country behave in a particular way.
For instance, I may have the stereotype that people from a particular country are loud and aggressive.
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x^3-6x^+2x-4 divided by x+2
Answer:
Step-by-step explanation:
find the answer to 9/16 in decimal form
Answer:
0.5625
Step-by-step explanation:
Quadrilateral ABCD is translated 5 units up. What are the coordinates of
quadrilateral A'B'C'D?
A
D
A(-5, 5)
D(-5, 1)
B' Y
G
C₁
8(-1,5)
C(1, 2)
OA. A'(-5, 0), B'(-1,0), C'(-1, -3),
D'(-5,-4)
OB. A'(-5, 10), B'(-1, 10), C'(-1,7),
D'(-5, 6)
C. A'(-10, 10), B'(-6, 10), C'(-6, 7),
D'(-10, 6)
D. A'(-10, 5), B'(-6, 5), C'(-6, 2),
D'(-10, 1)
Answer:
it should be B but I could be wrong
Step-by-step explanation:
B
can someone help me do this (will give brainliest if possible
Answer:
4) ∠1 and ∠2, ∠2 and ∠3
5) ∠1 and ∠3
6) x = 10
Step-by-step explanation:
Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.
Therefore, the pairs of adjacent angles in the given diagram are:
∠1 and ∠2∠2 and ∠3∠3 and ∠4∠4 and ∠5∠5 and ∠1Vertical angles are pairs of non-adjacent angles that are formed when two lines intersect. Vertical angles are congruent,
Therefore, the pair of vertical angles in the given diagram are:
∠1 and ∠3As ∠1 and ∠3 are the same measure:
⇒ m∠1 = m∠3
⇒ (9x)° = 90°
⇒ 9x = 90
⇒ 9x ÷ 9 = 90 ÷ 9
⇒ x = 10
Therefore, the value of x is 10.
Answer:
4) ∠1 and ∠2, ∠2 and ∠3.
5) ∠1 and ∠3.
6) x = 10.
Step-by-step explanation:
Explanations are given in attachment!
PLS HELP :))
The property taxes on a house were $1265
. What was the tax rate if the house was valued at $115,000
? Follow the problem-solving process and round your answer to the nearest hundredth of a percent, if necessary.
The tax rate of a house valued at $115,000 with a property tax of $1265 is 110%. or $110 per $1,000 of property value.
What is property tax?The property tax is the levy imposed on the assessed value of the property of an individual or corporation.
Property tax is usually levied as a percentage of the assessed value.
Data and Calculations:Property tax = $1265
House value - $115,000
Tax rate = 110% [tex](\$1265\div\$115000 \times 100)[/tex]
Thus, the tax rate of a house valued at $115,000 with a property tax of $115,000 is 110%. or $110 per $1,000 of property value.
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Calculate the area of the shape
Answer:
Step-by-step explanation:
Just divide the total shape into three shapes one rectangle and two triangles and then calculate the area
Hope this helps: )
Nathan rolls a number cube and records the result of each roll in the table.
Number Cube
Number Rolled
Frequency
1
11
2
16
3
14
4
20
5
12
6
17
Which statements below represent the situation? Select three options.
The correct three options are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
Nathan rolled the number cube a total of 90 times.
The number 4 was rolled more frequently than any other number.
The number 2 was rolled the least frequently of all the numbers.
The total number of rolls for odd numbers is greater than the total number of rolls for even numbers.
The correct statements are:
Nathan rolled a number cube and recorded the results in a table.
The number cube has six sides, numbered 1 through 6.
The number 4 was rolled more frequently than any other number.
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What is the price per bag of cookies
Answer: 6.3 per bag
Step-by-step explanation:
31.50 divided by 5 is 6.3!!!!
Answer: 6.3
Step-by-step explanation:
Divide 31.50 with 5
[tex]5\sqrt{31.50}[/tex]
5 goes into 3 0 times so you do 31/5. You get 6 with 1 as the remainder since 6x5 is 30. Now you do 15/5 which is 3. You get 63 but you have to add the decimal between the 6 and 3 so you will get 6.3. Hope this helped.
Alg 2 graphic quadratics in intercept form
The calculated key features of the quadratic functions 1 to 6 are listed below
Completing the key features of the graphsFunction 1: y = 1/2(x + 4)(x - 2)
Expand
y = x^2/2 + x - 4
From the function, we have
a = 1/2 (coefficient of x^2 term)
p = -b/2a (x-coordinate of the vertex)
p = -(1)/2(1/2)
p = -1
q = f(p) (y-coordinate of the vertex)
q = 1/2(1 + 4)(1 - 2)
q = -5/2
From the function, we have
x-intercepts = (-4, 0) and (2, 0)
This also means that the axis of symmetry is
x = -1
The quadratic function opens up because the coefficient of the x^2 term is positive.
Next, we have
Vertex = (-1, -5/2)
For the y-intercept, we have
y-intercept = f(0)
y-intercept = 1/2(0 + 4)(0 - 2)
y-intercept = -4
Slope to a point one unit from the vertex can be found by taking the derivative of the function:
f(x) = x^2/2 + x - 4
f'(x) = x + 1
At x = -2 (one unit to the left of the vertex), the slope is -1
i.e. f'(-2) = -2 + 1 = -1
At x = 0 (one unit to the right of the vertex), the slope is 1.
i.e. f'(0) = 0 + 1 = 1
When the above steps is repeated for the remaining functions, we have the following results:
Function 2: y = 1/2x(x - 8)
The features are:
a = 1/2, p = 4, q = -8x-intercepts = (0, 0) and (8, 0)Axis of symmetry: x = 4Opens up or down: UpVertex = (4, -8)y-intercepts = (0, 0)Slope to pt one unit from vertex: -1 and 1Function 3: y = (x + 2)(x - 2)
The features are:
a = 1, p = 0, q = -4x-intercepts = (-2, 0) and (2, 0)Axis of symmetry: x = 0Opens up or down: UpVertex = (0, -4)y-intercepts = (0, -4)Slope to pt one unit from vertex: -2 and 2Function 4: y = -1/3(x + 1)(x - 5)
The features are:
a = -1/3, p = 2, q = 3x-intercepts = (-1, 0) and (5, 0)Axis of symmetry: x = 2Opens up or down: DownVertex = (2, 3)y-intercepts = (0, 5/3)Slope to pt one unit from vertex: 2/3 and -2/3Function 5: y = 4(x + 2)(x + 1)
The features are:
a = 4, p = -3/2, q = -1x-intercepts = (-2, 0) and (-1, 0)Axis of symmetry: x = -3/2Opens up or down: UpVertex = (-3/2, -1)y-intercepts = (0, 8)Slope to pt one unit from vertex: -8 and 8Function 6: y = -(x - 3)(x - 3)
The features are:
a = -1, p = 3, q = 0x-intercepts = (3, 0)Axis of symmetry: x = 3Opens up or down: DownVertex = (3, 0)y-intercepts = (0, -9)Slope to pt one unit from vertex: 2 and -2Read more about quadratic functions at
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1
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day
How many more points did Zara score than John?
i
C
Number of Points
Points Scored in Basketball Game
25
20
15
10
5
0
e g
Read and Interpret Scaled Bar Graphs - Quiz - Level C
Mateo
Zara
Player
John
Mila
DONE
7
4
1
2
0
5
points
8
9
6
3
76°F Mostly cloudy
X
Th
Answer:
yes
Step-by-step explanation:
john has 34 marbles