Answer:
Year 2004
Step-by-step explanation:
Population of a country in year 1995 = 286
Model that expresses the growth rate of the population is,
P(t) = \(286(1.009)^{t-1995}\)
Here, t = year
a). For P = 311 million people
311 = \(286(1.009)^{t-1995}\)
\(\text{log}(\frac{311}{286})=\text{log}(1.009)^{t-1995}\)
log(311) - log(286) = (t - 1995)log(1.009)
2.4928 - 2.4564 = (t - 1995)(0.00389)
\(\frac{0.03639}{0.00389}=t-1995\)
t = 1995 + 9.4
t = 2004
In year 2004 population of the country will be 311.
2). Stuart took his wife out to dinner. The bill came to $72.00 and he
wants to leave a 15% tip. How much should Stuart leave the server for the
tip? *
Hellllpppppop!?!?!!?????
Answer:
10.8
Step-by-step explanation:
Answer:
$10.8
Step-by-step explanation:
First, you would multiply 72 x 15 to get 1,080. Then, you would divide 1,080 by 100 to get 10.8. I hope this helps :)
Pls help I’ll brainlest
Answer:
PLS GIVE BRAINLIEST
Step-by-step explanation:
\(50 + 7.50x\)
1. make an equation where x represents hours
\(50 + 7.50(5)\)
2. substitute 5 for x
\(50 + 37.5\)
3. multiply 7.50 by 5
\(87.5\)
4. add 50 and 37.5 to get 87.5
President Obama wrote a children's book about extraordinary Americans. One of those
Americans was Albert Einstein. One of Einstein's equations is shown below. Rearrange the
equation to solve for c
E = mc² where Eis energy, m is mass, and c is the speed of light
A) c = (E2 - m)1/2
B) c = E - m2
C) c = (E/m) 1/2
D) c = Em2
Evaluate the expression y - x + z for x = 4.7, y = 6, and z=0.68
y – X + z =
(Type an integer or a decimal.)
Answer:
1.98
Step-by-step explanation:
y - x + z for
x = 4.7, y = 6, and z=0.68
6 - 4.7 +.68
1.3+.68
1.98
Answer:
\(= 1.98 \\ \)
Step-by-step explanation:
given that,
\(x = 4.7 \\ y = 6 \\ z = 0.68\)
Let's solve now
\(y - x + z \\ 6 - 4.7 + 0.68 \\ 1.3 + 0.68 \\ = 1.98\)
Two times the sum of a number and 8 is negative 48 what is the number?
Answer:
-32
Step-by-step explanation:
Let the number be x.
\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)
1. Use the Pythagorean
Theorem to determine if a
triangle with side lengths 6ft.,
6ft., 8ft. is a right triangle.
Answer:
Not a right triangle
Step-by-step explanation:
\( {6}^{2} + {6}^{2} = 36 + 36 = 72...(1) \\ \\ {8}^{2} = 64....(2) \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ {6}^{2} + {6}^{2} \neq {8}^{2} \\ \\ \)
Hence, triangle with side lengths 6ft.,
6ft., 8ft. is not a right triangle.
If (-1, y) lles on the graph of y = 3x+1, then y =
Answer:
y = -2
Step-by-step explanation:
Plug in x = -1
y = 3(-1) + 1
y = -3 + 1
y = -2
Please Help practice #3
Answer:
(2x+5)(4x+3)
Step-by-step explanation:
Given the expression 8x^2 + 26x + 15
Factorize
8x^2 + 26x + 15
= 8x^2 + 6x + 20x + 15
= 2x(4x+3) + 5 (4x+3)
= (2x+5)(4x+3)
Hence the factored form of the expression is (2x+5)(4x+3)
2x-1=y
3x-1=y
Consider the system of equations above. Which of the following statements about this system is true?
Answer:
B; There is only one (x,y) solution and y is negative
Step-by-step explanation:
First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.
If this answer helped you, please leave a thanks!
Have a GREAT day!!!
Deon throws a ball into the air. The height h of the ball, in meters, at time t seconds is modeled by the function h(t)=-5t^2+2t+39
Will the ball reach height of 41 meters. What is the discriminate?
Please help me, please
Answer:
The ball will not reach a height of 41 meters.
The discriminate is 784
Step-by-step explanation:
You know that the height h of the ball, in meters, at time t seconds is modeled by the function h(t) = - 5*t² + 2*t + 39
To find out if the ball will reach a height of 41 meters, you must calculate the maximum of the function, that is, the highest or highest point on the graph. That is, the maximum in a function f is the largest value that the function takes.
The vertex is a point that is part of the parabola, which has as its ordinate the maximum value (as in this case) or minimum value of the function. That is, the vertex is the maximum of the function (as in this case) or minimum.
In this case, the maximum of t is obtained by:
\(t=\frac{-b}{2*a}\)
Being a=-5 and b=2 (comparing with a quadratic function of the form: f(x)=a*x² + b*x +c)
\(t=\frac{-2}{2*(-5)}\)
t= 0.2
The maximum height value must be obtained by substituting the previously calculated value of t in the function:
h(0.2) = - 5*0.2² + 2*0.2 + 39
h(0.2)=39.2
So the maximum height the ball will reach is 39.2 meters. The ball will not reach a height of 41 meters.
The discriminate of a quadratic function is:
Δ=b²-4*a*c
In this case, being a=-5, b=2 and c=39, the discriminate is:
Δ=2²-4*(-5)*39
Δ= 4+780
Δ= 784
The discriminate is 784
The first derivative test is the process of analyzing functions using their first derivatives in order to find their extreme point.
No, ball can not reach at height of 41 meters.
Since, The height h of the ball, in meters, at time t seconds is modeled by the function \(h(t)=-5t^2+2t+39\)
To find maximum height where can ball reach. We use first and second derivative test.
\(h(t)=-5t^2+2t+39\\\\\frac{dh}{dt}=-10t+2\)
Now, equate above derivative to zero.
\(-10t+2=0\\\\t=1/5\)
Now, find second derivative
\(\frac{d^{2}h }{dt^{2} } =-10\) , Which is less than zero.
Therefore, at t= 1/5 second , will give maximum height that can ball reach.
So, h(1/5) = 39.2 meters.
That is, ball can reach at 39.2 meters.
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Find area of trapezium with height 8cm and the sum of its parallel sides as 15cm
Answer:
The Area of the trapezium is \(60cm^2\)
Step-by-step explanation:
Given,
Height (h)= 8cm
Sum of the parallel sides (a+b)= 15cm
Area of trapezium = \(1/2*h*(a+b)\)
=\(1/2*8*15\)
=\(4*15\)
Area of trapezium=60cm^2
Answer: Area = 60 cm²
Step-by-step explanation:
To find the area of a trapezium we use the formula
Area of trapezium = 1/2 (sum of parallel sides) × height
∴ Area = 1/2 ×15 cm × 8 cm
= 60 cm²
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How can the following expression be simplified and written without negative exponents
On solving the provided question we can say that the expression is \(b^{-17}b^{11} / b^{-5}\)=> \(b^{-17}b^{11} b^{5}\)=> \(b^{-17}b^{16}\) => \(1/b\)
what is expression ?You can double, divided, add, or take something away in mathematics. An expression is put together as follows: Expression, numeric value, and math operator A mathematical expression is composed of numbers, parameters, and functions Contrasting phrases and expressions is possible. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and a mathematical action between them. As an illustration, the phrase 4m + 5 consists of the phrases 4m and 5, together with the given equation's variable m, which are all split by the mathematical sign.
the expression is
\(b^{-17}b^{11} / b^{-5}\)
=> \(b^{-17}b^{11} b^{5}\)
=> \(b^{-17}b^{16}\)
=> \(b^{-1}\)
=> \(1/b\)
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a rectangle with a width of 30 centimeters has a perimiter of 100 centimeters to 160 centimeters graph a compound inequality
Answer:
5 ≤ L ≤ 35
Step-by-step explanation:
Let w represent the width of the rectangle.
The perimeter (P) of the rectangle is given by:
P = 2w + 2L
Where L is the length of the rectangle.
We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:
100 ≤ 2(30) + 2L ≤ 160
100 ≤ 90 + 2L ≤ 160
10 ≤ 2L ≤ 70
We can now divide both sides by 2 to solve for L:
5 ≤ L ≤ 35
Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is: 5 ≤ L ≤ 35
A piece of wire 18cm long is bent to form a rectangle. If its length is x cm, obtain an expression for its area in terms of
* and hence calculate the dimensions of the rectangle with maximum area
Answer:
To form a rectangle, the piece of wire will have two sides of length x and two sides of length (18 - 2x)/2 = 9 - x. Therefore, the perimeter of the rectangle is given by:
2x + 2(9 - x) = 18 - 2x
The area of the rectangle is given by:
A = x(9 - x)
Expanding this expression, we get:
A = 9x - x^2
To find the dimensions of the rectangle with maximum area, we can differentiate the area expression with respect to x:
dA/dx = 9 - 2x
Setting this equal to zero to find the maximum:
9 - 2x = 0
x = 4.5
So, one side of the rectangle is x = 4.5 cm and the other side is (18 - 2x)/2 = 4.5 cm. Therefore, the dimensions of the rectangle with maximum area are 4.5 cm by 4.5 cm.
To calculate the maximum area, we can substitute x = 4.5 into the area expression:
A = 9(4.5) - (4.5)^2 = 20.25 cm^2
Step-by-step explanation:
Rumus suatu fungsi di nyatakan dengan f (x) = 2x + 5. Jika f(a) = 7, nilai a adalah
Step-by-step explanation:
As my previous answer got deleted for being wrong (in which it was right), I will answer again.
The answer is 1. Why? Just plug it into the equation. F(1) = 2(1) + 5 = 7.
This is proof that it is right, and that there are some corrupt admins on brainly.
How to get to this solution?
Well notice how we are given what f(a) is. It is 2a + 5. So plug this in for f(a).
If we do so, we get 2a + 5 = 7.
Solving this equation, we get a = 1.
An airplane has an airspeed of 528 mi/hr bearing 25° west of north. Which of the following vectors best describes the path of the airplane? O v= 528 cos(155°)i + 528 sin(1550); O v = 25 cos(528°)i + 25 sin(528°); O None of these O v = 528 cos(25°)i + 528 sin(259); O v = 528 cos(115°)i + 528 sin(115)
An airplane has an airspeed of 528 mi/hr bearing 25⁰ west of north. The path can be described as a vector v = (528 cos 115⁰) i + (528 sin 115⁰) j
Suppose we have a vector with magnitude v and angle α with the positive x-axis, then the vector can be expressed as its component as:
vx = v cos α
vy = v sin α
or
v = vx i + vy j
v = (v cos α) i + (v sin α) j
In the given problem, the magnitude is 528, while the angle is:
α = 25⁰ west of north = 25⁰ + 90⁰ = 115⁰
Hence,
vx = 528 cos 115⁰
vy = 528 sin 115⁰
v = (528 cos 115⁰) i + (528 sin 115⁰) j
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. Mildred bought an old
necklace and pair of earrings
while at an antique show. If
the cost of the jewelry is ]
and tax is 7%, which of the
following equations could be
used to find the total cost of
the jewelry?
a. .07 + ]
b. J +.07 x)
C. (.07x)) + ]
d. 7) + ]
Answer:
j * .07 +j
Step-by-step explanation:
The tax on the jewelry is J* .07
Add the tax to the cost of the jewelry to get the total cost
j * .07 +j
Find the most appropriate units to measure John’s waist.
can someone please help? the question is in the picture.
Answer: b
Step-by-step explanation: a right triangle should have a right angle so you´d need atleast one right angle and two acute angles.
the shape is a rectangular prism. find the lateral surface area of the shape. then enter your answer without units below.
The lateral surface area of a rectangular prism is 2(l + w)h sq units.
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces).
All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. The lateral surface area of a rectangular prism is the sum of the surface area of all its faces without the base of the rectangular prism. The lateral surface area of any right rectangular prism is equivalent to the perimeter of the base times the height of the prism.The lateral surface area of a rectangular prism is given by
2(l + w)h sq unitsWhere l, w, and h are the length, width, and height, respectively. To find the lateral surface area, we need the values of l, w, and h.
Without these values, it is not possible to determine the lateral surface area of the rectangular prism.
Therefore, the lateral surface area of a rectangular prism is 2(l + w)h sq units.
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He buys atoy car for 150 the sells it for $120find his percentage loss
Answer: 80%
Step-by-step explanation:
divide 120 by 150 and you get .8 then you move the decimal over 2
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
The line parallel to the x-axis passing through the points (5,5) and (-5,5) has a slope of 0, indicating a horizontal line with a constant y-coordinate value of 5.
To determine the slope of the line that represents this relationship, we can use the formula for slope, which is given by:
slope = (change in y-coordinates) / (change in x-coordinates)
In this case, we are given two points on the line: (5,5) and (-5,5).
The change in y-coordinates is 5 - 5 = 0, as the y-coordinate remains constant.
The change in x-coordinates is -5 - 5 = -10.
Substituting these values into the slope formula, we get:
slope = 0 / -10 = 0
Therefore, the slope of the line that represents this relationship is 0.
A slope of 0 indicates that the line is parallel to the x-axis. This means that the line has a constant y-coordinate value for all x-coordinate values. In this case, the line passes through the point (5,5) and (-5,5), and it remains at y = 5 for all x-values.
Visually, a line with a slope of 0 would be a horizontal line on the coordinate plane. It does not have an upward or downward slope but remains parallel to the x-axis.
It's important to note that the slope of 0 indicates a relationship where the dependent variable (y) does not change with respect to the independent variable (x). In this case, no matter the value of x, the corresponding y-value remains constant at 5.
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A 15 meter long cylinder with a diameter of 7 meters has a square prism with a base length of 4 meters hole going all the way through the center of it as shown in the diagram (not to scale). Find the volume of the composite shape rounding to the nearest cubic meter.
Answer:
The volume of the composite figure is approximately 337.27 m³
Step-by-step explanation:
The given parameters are;
The length of the cylinder, L = 15 meters
The diameter of the cylinder, D = 7 meters
The base length of the square prism, B = 4 meters
We note that the square diagonal of the square = √(4² + 4²) = 4·√2 ≈ 5.66 meters, fits in the cylinder
Therefore, we have;
The volume of the composite figure = The volume of the cylinder - The volume of the square prism
The volume of the cylinder = π/4 × D² × L = π/4 × 7² × 15 ≈ 577.27 m³
The volume of the square prism = B² × L = 4² × 15 = 240 m³
∴ The volume of the composite figure ≈ 577.27 m³ - 240 m³ ≈ 337.27 m³
The volume of the composite figure ≈ 337.27 m³.
Tax in New Jersey is 7%. If you spend $120 on a shopping spree, how much does the tax cost? Show your work
in the space provided.
Answer:
$8.40
Step-by-step explanation:
120 * 7% = $8.40
make 2 2/5% a fraction in simplest form
Answer: 3/125
Step-by-step explanation:
Answer:
24/1000
Step-by-step explanation:
Step 1:
2 2/5% = 2.4%
Step 2:
2.4% = 0.024
Step 3:
0.024 = 24/1000
Answer:
24/1000
Hope This Helps :)
you could at least answer the question not say why should anyone care about a school bus
Answer:
Step-by-step explanation:
I think anyone needs to care about the school bus, it's just a bus, and maybe the people inside are like you, so relax, keep calm on a school bus
Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither.
f(x)=x³ - 2x
Answer: The function is odd and symmetric with respect to the origin.
Step-by-step explanation:
A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.
\(f(x)=x^{3}-2x\\\\f(-x)=(-x)^{3}-2(-x)=-x^{3}+2x=-f(x)\)
Therefore, the function is odd, and thus the function is symmetric about the origin
Enter the number that belongs in the green box
The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:
\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)
49 = 16 + 25 - 40*cos(C)
49 = 41 - 40*cos(C)
40*cos(C) = 41 - 49
40*cos(C) = -8
cos(C) = -8/40
cos(C) = -0.2
To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:
C = arccos(-0.2)
Using a calculator, we find that C ≈ 101.54 degrees.
Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
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Which rule(s) represents a linear function?
Answer:
f(x) = ax + b, where a and b are real numbers.
fine the nth term of 11,13,15,17
The nth term of 11,13,15,17 is,
⇒ T (n) = 9 + 2n
Given that;
The sequence is,
11, 13, 15, 17, ....
Here, Common difference is,
13 - 11 = 2
15 - 13 = 2
Hence, Sequence is in Arithmetic sequence.
So, the nth term of 11,13,15,17 is,
⇒ T (n) = a + (n - 1)d
⇒ T (n) = 11 + (n - 1) 2
⇒ T (n) = 11 + 2n - 2
⇒ T (n) = 9 + 2n
Thus, The nth term of 11,13,15,17 is,
⇒ T (n) = 9 + 2n
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