Answer:
Step-by-step explanation:
Area of a rectangle = length times width.
Area of the garden = 6z(4z + 17)
24z² + 102z
Annie made 4 glasses of juice,her 5 friends drank 1/2 glass each.what fraction of juice was left? how to solve it
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank [tex]\frac{1}{2}[/tex] glass each.
Meaning of fraction = An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
Annie made 4 glasses of juice
To find = fraction of juice that was left
Total glasses of juice = 4
Her 5 friends drank 1/2 glass each
= 5 × [tex]\frac{1}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
Fraction of juice that left,
5 - [tex]\frac{5}{2}[/tex]
Subtracting by taking LCM,
= [tex]\frac{10 - 5}{2}[/tex]
= [tex]\frac{5}{2}[/tex]
[tex]\frac{5}{2}[/tex] juice was left when Annie made 4 glasses of juice, her 5 friends drank 1/2 glass each.
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When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive $140 for lodging plus $0.60 per mile driven. How many miles did Joe drive if his company reimbursed him $290 for an overnight trip?
Question content area bottom
Part 1
The equation is enter your response here. Joe drove enter your response here miles.
(Type an equation using x as the variable.)
solve for equation and miles Joe drove
Joe was given $329 for an overnight trip because he drove a distance of 220 miles
How to solve Word Problems ?
Five Easy Steps to Solving Word Problems (WASSP)
Write (or draw) what you know.Ask the question.Set up a math problem that could answer the question.Solve the math problem to get an answer.Put the answer in a sentence to see if the answer makes sense!Given Data
Amount rep receive = $175
Added amount per mile driven = $0.70
Reimbursed/Total = $329
The Mathematical relation for this scenario is
Total amount = Amount Receive+ 0.7*Distance driven
let the distance driven be x
Substituting our given data into the relation we have
329= 175+ 0.7*x
329-175 = 0.7x
154 = 0.7x
divide both sides by 0.7
x = 154/0.7
x = 220miles
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Drag figures and equations to the table to show the net and surface area of the rectangular prism.
The numbers are
W = 3cm.
I = 6cm.
H =3cm.
Pleaseee helppp
According to the posed question, the rectangular prism's surface area would be 90 cm2.
What is a Rectangular Prism's Surface Area?
The total surface area of a rectangular prism's rectangular faces is alluded to as the prism's surface area. There are two distinct types of it: lateral surface area and total surface area. In contradiction to the lateral surface area, which only includes the lateral faces and omit the base areas, the total surface area of a rectangular prism refers to the area among all six faces.
Given, W = 3 cm, L = 6 cm, and H = 3 cm
surface area = 2 (WL + LH + HW)
= 2 (18 + 18 + 9)
= 2× 45 = 90 cm².
Consequently, the rectangular prism's surface area is 90 cm².
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Use the data in the table below, which shows the employment status of individuals in a particular town by age group.
Age
0-17
18-25
26-34
35-49
50 +
Full-time
21
267
492
535
520
Part-time
187
200
67
195
166
Unemployed
356
135
28
133
231
If a person is randomly chosen from the town's population, what is the probability that the person is under 18 or employed part-time?
X
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The probability that the person is under 18 or employed part-time is 179/864.
What is experimental probability?Experimental probability calculates the probability of some event from the results of experiments.
For an event E, we get the experimental probability of that event
[tex]P_e(E) = \dfrac{\text{Number of times E occurred}}{\text{Number of times experiments was done}}[/tex]
where,[tex]P_e(E)[/tex] is denoting experimental probability of occurrence of E.
Given that;
The table of age, full time, part time, unemployed
Now,
Total number of people who are between the age group 35-49
= 581+179+104
= 864
Number of people who are employed part time= 179
Number of people employed part time in age group 35-49/ Total people in age group 35-49
= 179/864
Therefore, the probability will be 179/864.
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A business puchases a computer system for $3,000. The value of the system decreases at a rate of 15% per year. Write an exponentioal function to model this situation. Then determine how much the comoputer will be work after 3 years
Value of system after 'x' years = [tex]3000*(0.85)^x[/tex]
The value of the computer after 3 years is $1842.375
What is an exponential function?The formula for an exponential function is f(x) =[tex]a^x[/tex], where 'x' is variable and 'a' is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
Given that, computer system values at $3000 decrease at a rate of 15% each year.
If the value decreases by 15%, it means that the new value is 85% of the old value.
new value = old value * (85/100)
new value = old value * 0.85
value in 1st year = $3000
value after 1st year = $3000 * 0.85
value after 2nd year = $3000 * 0.85 * 0.85
value after nth year = $3000 * [tex]0.85^n[/tex]
Value of the system after 3 years = $3000 * [tex]0.85^3[/tex]
= $3000 * 0.614125
= $1842.375
Therefore, The value of the computer system after 3 years is $1842.375
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help me find the measure
Answer:
= 60°
Step-by-step explanation:
Exterior angle =
[tex] = \frac{360}{n} [/tex]
[tex] = \frac{360}{6} \\ = {60}^{o} [/tex]
= 60°
-
The function f(x) = |x − 1| can be used to determine how far a number is away
from the number 1 on the number line. Find and interpret the given function values
and determine an appropriate domain for the function.
number line showed for reference
←
-5 -4 -3
-2 -1
O
2 3
f(-5) =
meaning the number
from 1 on the number line. This interpretation
context of the problem.
f(3) =
1 on the number line. This interpretation
the problem.
4 5
is a distance of
meaning the number is a distance of
units away
in the
units away from
in the context of
Answer:
Step-by-step explanation:
The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.
To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.
For example, let's find f(-5):
f(-5) = |-5 - 1| = |-6| = 6
The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.
Now let's find f(3):
f(3) = |3 - 1| = |2| = 2
The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.
The domain of the function is all real numbers. The range of the function is all non-negative real numbers.
Two gliders collide on an air track. Glider 1 has a mass of 7. 0 kg, and glider 2 has a mass of 4. 0 kg. Before the collision, glider 1 had a velocity of 2. 0 m/s, and glider 2 had a velocity of -5. 0 m/s. If the collision is perfectly elastic, what is the total kinetic energy of both gliders after the collision?
A. -36. 0 J
B. 36. 0 J
C. 64. 0 J
D. 128. 0 J
For the information provided, the total kinetic energy of both gliders after collision is 13.5 J. In an elastic collision, both momentum and kinetic energy are conserved.
The momentum conservation principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. Mathematically, we can write this as:
m₁v₁i + m₂v₂i = m₁v₁f + m₂v₂f
where m₁ and v₁i are the mass and initial velocity of glider 1, m₂ and v₂i are the mass and initial velocity of glider 2, and v₁f and v₂f are their velocities after the collision.
Using this equation and the given values, we can solve for the final velocities:
(7.0 kg)(2.0 m/s) + (4.0 kg)(-5.0 m/s) = (7.0 kg)v₁f + (4.0 kg)v₂f
14.0 kg·m/s - 20.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f
-6.0 kg·m/s = 7.0 kg·v₁f + 4.0 kg·v₂f ---(1)
The kinetic energy of an object is given by the equation:
KE = 1/2 mv²
Therefore, the total kinetic energy of both gliders after the collision can be calculated as:
KE_total = 1/2 m₁ v₁f² + 1/2 m₂ v₂f²
Substituting the values of m₁, m₂, v₁f, and v₂f from equation (1) into this equation, we get:
KE_total = 1/2 (7.0 kg) (0.86 m/s²) + 1/2 (4.0 kg) (5.14 m/s²)
KE_total = 13.5 J
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Interpret the scatter plot based on the shape of the distribution.
Answer: Looks like a positive correlation with an outlier in the lower left.
Step-by-step explanation:
For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
The constant of proportionality is
An equation that relates the total cost y and the number of lemons x is y=____x
Use the equation you wrote to complete the table.
Answer:
he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.
The equation that relates the total cost, y, and the number of lemons, x, is:
y = 1.80 * (x/3) + b
where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.
Here is a table with the values of y and x, assuming b = 0:
x (Number of Lemons) y (Total Cost)
0 0
3 1.80
6 3.60
9 5.40
... ...
Step-by-step explanation:
Winnie made headbands to sell at the school craft fair. She sells each
headband for $6.25 and her goal is to earn at least $50.00. Write and solve
an inequality to represent this situation, where h represents the number
of headbands Winnie must sell in order to reach her goal.
Answer:
6.25 x h = 50.000
Step-by-step explanation:
Answer:
8 headbands.
Step-by-step explanation:
Winnie needs to sell AT LEAST 8 headbands. 50 divided by 6.25 is 8. Remember that the phrase "at least" is represented by a greater-than-or-equal-to symbol.
Shaun White, the Flying Tomato, is rolling down a 30° ramp on his skateboard (because he's not just a snowboarding gold medalist, the bro can skate too). The total mass of Shaun and his skateboard is 75 kg. The rolling friction between the skateboard wheels and the concrete is 9N acting backward against the skateboard. The drag force due to air resistance is 11 N acting backwards against Shaun. What is Shaun's acceleration? 30° 4.64 m/s2 down the slope
Previous question
If the drag force due to air resistance is 11 N acting backwards against Shaun. Shaun's acceleration is 4.64 m/s^2 down the slope.
To find Shaun's acceleration, we need to calculate the net force acting on him and his skateboard. The net force is the vector sum of all the forces acting on the object. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and its acceleration:
Net force = mass × acceleration
Let's break down the forces acting on Shaun and his skateboard:
The force of gravity, which acts vertically downwards with a magnitude of mg, where m is the total mass of Shaun and his skateboard and g is the acceleration due to gravity (9.8 m/s^2).
F₁ = m * g * sin(30°) = 75 kg * 9.8 m/s^2 * sin(30°) = 367.5 N
The force due to rolling friction between the skateboard wheels and the concrete, which acts backward against the skateboard.
F₂ = 9 N (given)
The drag force due to air resistance, which acts backward against Shaun.
F₃ = 11 N (given)
Now, let's add up the forces to get the net force:
Net force = F₁ - F₂ - F₃
= 367.5 N - 9 N - 11 N
= 347.5 N
Using Newton's second law of motion, we can now calculate Shaun's acceleration:
acceleration = Net force / mass
= 347.5 N / 75 kg
= 4.64 m/s^2 (down the slope)
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The relationship between the amount of energy released by an earthquake and its magnitude is described by this formula. Here E is energy, in joules, and M is magnitude. Approximately how much energy is released by a magnitude 5 earthquake? Select the correct answer.logE=5.24+1.44M
Approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.
What is a logarithmic equation?A logarithmic equation is an equation that involves a logarithmic function. A logarithmic function is the inverse of an exponential function, and it represents the exponent to which a given base must be raised to obtain a given number.
The formula that relates the energy released by an earthquake to its magnitude is given by:
logE = 5.24 + 1.44M
To find the amount of energy released by a magnitude 5 earthquake, we can substitute M = 5 into the formula and solve for E.
logE = 5.24 + 1.44(5)
logE = 5.24 + 7.2
logE = 12.44
Now we need to convert this logarithmic value to a regular value of E. We can do this by taking the antilogarithm (or exponentiating) both sides of the equation.
10⁽ˡᵒᵍᴱ⁾ = 10⁽¹²ॱ⁴⁴⁾
E = 2.51 x 10¹² joules
Therefore, approximately 2.51 x 10¹² joules of energy is released by a magnitude 5 earthquake.
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How can i put this in slope intercept form?
X int= 5; Y int= -2
Help, please thank you, and have a wonderful day
For a particular 4 leaf clover, the highway had to be compacted on the south side making the circles two different sizes. The two circles on the north of the highway have a radius of 128 feet and the two on the south side have radius of 102 feetCalculate the total area of grass seed needed for these four circles
The total area of the two circles will be 168316.9 square feet.
What is a circle?The circle is defined as a two-dimensional figure having a fixed point and the number of the points is traced around the curved path at an equal distance from the fixed point. The overall figure is called a circle.
The area of the circle is calculated by the formula:-
Area = πr²
Given that the south side of the highway needed to be compacted in order to create two circles of various sizes for a specific four-leaf clover. The two circles on the north side of the road have a 128-foot radius, whereas the two on the south side have a 102-foot radius.
The total area will be calculated as:-
Area = 2 x π x 128² + 2 x π x 102²
Area = 102943.25 + 65370.25
Area = 168316.9 square feet
Hence, the total area will be 168316.9 square feet.
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Choose all of the values that are solutions to inequality x < -2
Answer:
The solution to the inequality x < -2 is all real numbers that are less than -2. This means that any number that is less than -2 will satisfy the inequality, but any number that is greater than or equal to -2 will not.
So, the solution set for x < -2 is all real numbers that are less than -2. This solution set can be expressed as (-∞, -2).
Therefore, the values that are solutions to the inequality x < -2 are:
• all real numbers less than -2, such as -3, -4, -5, etc.
Note that -2 itself is not part of the solution set, since it is not less than -2.
what is 7/8 of 16 times in half of 30?
The simplification of the given expression would be = 210
How to simplify the given expression above?A fraction is defined as the expression of part of a whole value in the form of a denominator and a numerator.
The above statement can be expressed above mathematically as follows:
= 7/8 × 16 × 1/2× 30
= 3360/16
= 210
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Find the 96th term of the arithmetic sequence 1, -12, -25
Answer:a
Step-by-step explanation:
The average mass of a certain type of microorganism is 2.4×10^ −6
grams. What is the approximate total mass of 5,000 of these microorganisms?
0.0012 g
0.012
0.12 g
0.00012 g
Answer:
Below
Step-by-step explanation:
5000 * 2.4 x 10^-6 =
12 000 x 10^-6 g
= .012 g
Help!!! I can’t even find the answer for this question
Answer:
<1 and <2
Step-by-step explanation:
Adjacent means angles that are next to each other. This is not the only pair, but <1 and <2 are adjacent.
The first term of an ap is 29 and the seventh term is -13 what is the value of the tenth term
Step-by-step explanation:
an arithmetic progression or arithmetic sequence is a sequence of terms, where the difference bergen neighboring terms is a constant d for the whole sequence.
a1 = 29
a2 = 29 + d
a3 = a2 + d = a1 + d + d = 29 + 2d
...
an = 29 + (n-1)d
a7 = -13 = 29 + 6d
-42 = 6d
d = -42/6 = -7
therefore,
a10 = 29 + 9×-7 = 29 - 63 = -34
Select all of these coordinates that lie on the
line y = 1-2x.
(-5, -9) (-3,7) (4,9) (6, -11)
The coordinates that lie on the equation of line y = 1 - 2x are P ( -3 , 7 ) and Q ( 6, -11)
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , 7 )
Let the second point be Q ( 6 , -11 )
The equation of line is y = 1 - 2x
Substituting the values of x and y in the equation , we get
when x = -3
y = 1 - 2 ( -3 )
y = 1 + 6
y = 7
when x = 6
y = 1 - 2 ( 6 )
y = 1 - 12
y = -11
Hence , the coordinates of the equation of line are P ( -3 , 7 ) and Q ( 6, -11 )
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Please helpppp!!!!!!
Step-by-step explanation:
On the region, (-oo,0.5), the graph formes a upside U shaped , this mean the graph is concave down on this region. this implies that our second derivative is negative and our first derivative is changing negatively.
The graph is concave up from (0.5,oo) since the graph formes a U shape.
This also implies that (0.5) is a inflection point
The function crosses the x axis at -1,0,3
So the 2nd,3rd,6th, 7th options are correct
Solve the inequality √x+2 > -1.
The final inequality is x > - 1.
Option D is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
√(x + 2) > -1
Squaring both sides.
x + 2 > (-1)²
x + 2 > 1
Subtracting 2 on both sides.
x > 1 - 2
x > -1
Thus,
x > - 1 is the final inequality.
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Consider the line 8x-5y=1
what is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line
Answer:
[tex]\frac{8}{5}[/tex] and - [tex]\frac{5}{8}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
8x - 5y = 1 ( subtract 8x from both sides )
- 5y = - 8x + 1 ( divide through by - 5 )
y = [tex]\frac{8}{5}[/tex] x - [tex]\frac{1}{5}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{8}{5}[/tex]
• Parallel lines have equal slopes
then the slope of a parallel line is m = [tex]\frac{8}{5}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{8}{5} }[/tex] = - [tex]\frac{5}{8}[/tex]
create a table of values to represent the total cost if ben orders 1 or 2 books or spends 41$, $65 OR $125
The table to represents the total cost for the different numbers of books ordered is:
Number of books Spending Total cost
1 $41 $44
2 $65 $71
3 $125 $134
What is an expression?An expression is written with one or more terms with addition, subtraction, multiplication, and division.
Example:
2.2 + 3x + 4y = 7 is an expression.
3 + 5x = 9 is an expression.
We have,
The book cost = $3
Now,
Spendings = $41, $65, or $125
Now,
Table:
Number of books Spending Total cost
1 $41 41 + 3 = $44
2 $65 65 + 6 = $71
3 $125 125 + 9 = $134
Thus,
The table for the total cost is given above.
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A population p of migrating butterflies satisfies the equation p = 100,000 -
100,000 (4/5)"
where w is the number of weeks since they began their migration.
Complete the table with the population after different numbers of weeks.
W
р
0
100000
1
20000
2
4000
What is the vertical intercept of the graph?
800
3
160
The vertical intercept of the graph is 100,000
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e, is called an exponential function.
Given that, the population p of migrating butterflies satisfies the exponential function p = 100,000 (4/5)ⁿ, where n is the number of weeks,
So, we need to find the vertical intercept of the graph,
We know that, vertical intercept = intercept
To find the y-intercept of a line, we will put x = 0,
here x is n,
So, the y-intercept of the graph is = 100,000 (4/5)⁰ = 100,000×1 = 100,000
Therefore, the vertical intercept of the graph is 100,000
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Claudia records the hours is been studying and a test scores for five test
The correlation coefficient when Claudia records the hours she spent studying and her test scores for 5 tests is 0.85. This is a strong positive correlation.
How to explain the correlationAny statistical association between two random variables or bivariate data, whether causal or not, is referred to as dependence or correlation.
Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation. Theoretically, the same external forces can affect both of these separate variables because they travel in the same direction.
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Claudia records the hours she spent studying and her test scores for 5 tests.
What is the correlation coefficient?
-0.85-0.840.840.85
What is the strength of the model?
For every point on the graph of f(x), there is a point on the graph of F^-1(x) with reversed coordinates. TRUE or FALSE
you will get 40 points for answering it!
The statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.
What is inverse function?In relation to the original function f, the inverse function is denoted by the symbol f⁻¹, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.
We know that inverse of function is NOT the reciprocal of f. The composition of the function f and the reciprocal function f inverse gives the domain value of x.
Hence, the statement, For every point on the graph of f(x), there is a point on the graph of F⁻¹(x) with reversed coordinates is false.
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