We can use the exponential function [tex]N(t) = N0 * 2^(t/2)[/tex] to determine the number of transistors in a car that doubles every two years.
An exponential function with the following form can be used to calculate the number of transistors in an automobile whose number doubles every two years:
[tex]N(t) = N0 * 2^(t/2)[/tex]
Where t is the amount of time in years after the initial measurement, N0 is the number of transistors at the start, and N(t) is the number of transistors at time t.
We can use this technique to determine the number of transistors in the car in any odd year since 1974, when there were 4100 in it.
For instance, we may insert in t = 15 to determine the quantity of transistors in 1989:
transistors N(15) = 4100 * 2(15/2) = 261,632
Similarly, we may enter t = 19 to calculate the number of transistors in 1993:
522,724 transistors are found in N(19) = 4100 * 2(19/2)
In 1997, we can enter t = 23:
1,045,449 transistors make up N(23) = 4100 * 2(23/2)
In summary, we may calculate the number of transistors in an automobile whose number doubles every two years using the exponential equation [tex]N(t) = N0 * 2(t/2)[/tex]. We can determine the number of transistors in a car in any odd year with an initial measurement of 4100 transistors in 1974.
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The path of the basketball is modeled by the equation h() = −.25 + 2 + 4 where t is the time in seconds and h(t) is the height of the basketball at time t. What type of vertex (minimum or maximum) would this quadratic function create? Explain, using any method, how you found your answer.
To determine the type of vertex created by this quadratic function, we need to find the vertex of the parabola. The vertex of a parabola is the point where the parabola reaches its minimum or maximum value.
What is the vertex of a quadratic function?The given equation [tex]h(t) = -0.25t^2 + 2t + 4[/tex] represents the height of the basketball as a function of time.
The vertex of a quadratic function in the form of [tex]f(x) = ax^2 + bx + c[/tex] can be found by using the formula:
[tex]x = -b/2a[/tex]
[tex]y = f(x) = a(x^2) + bx + c[/tex]
where (x,y) is the vertex of the parabola.
Comparing this with the given equation [tex]h(t) = -0.25t^2 + 2t + 4[/tex] , we see that a = -0.25, b = 2, and c = 4.
Substituting these values in the formula, we get:
[tex]t = -2/(2\times(-0.25)) = 4[/tex]
[tex]h(4) = -0.25(4)^2 + 2(4) + 4 = 6[/tex]
Therefore, the vertex of the parabola is [tex](4, 6)[/tex] . Since the coefficient of the t^2 term is negative, the parabola opens downwards, and the vertex represents the maximum point of the parabola. The quadratic function [tex]h(t) = -0.25t^2 + 2t + 4[/tex] would create a maximum vertex.
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In the diagram below, find the indicated segment length. Assume that lines or segments which appear to be tangent are tangent.
Step-by-step explanation:
16 is tangent and the radial (12) is perpendicular
so this is a right triangle
Use Pythagorean theorem
?^2 = 12^2 + 16^2
?^2 = 400
? = 20 units
In a tuition centre 70% students have studied Maths and 30% have studied English. If all the students who study English also study Maths and 150 did not study both the subjects, find the number of students who study Maths but not English.
Maceeey's family wants to buy a new desktop computer. The sides of the screen are 20 inches by 24 inches. What is the diagonal of the screen?
Which graph represents the function f (x) = 3 +4?
The graph that closely matches the function is graph C.
Para jugar un juego, se lanza un cubo con cuatro caras numeradas del 1 al 6 y se lanza una moneda imparcial. ¿Cuál es la probabilidad de que caiga en cara y sacar un 3 o un 5?
El cubo tiene cuatro caras numeradas del 1 al 6, lo que significa que hay un total de 4 posibles resultados en los que se puede obtener un 3 o un 5.
La moneda tiene dos caras, y dado que es imparcial, hay una probabilidad del 50% de que caiga en cara.
Entonces, la probabilidad de que se lance el cubo y la moneda al mismo tiempo y se obtenga un 3 o un 5 y una cara es igual a la probabilidad de obtener un 3 o un 5 multiplicada por la probabilidad de obtener una cara en la moneda.
La probabilidad de obtener un 3 o un 5 es de 2/6, o 1/3. La probabilidad de obtener una cara en la moneda es de 1/2.
Por lo tanto, la probabilidad total es:
1/3 x 1/2 = 1/6
La probabilidad de que caiga en cara y sacar un 3 o un 5 es de 1/6 o aproximadamente 0.1667.
Please lmk asap, I’m so lost.
The complete table is:
x f(x)
-8 -8
-1 -8
1 -8
And the graph can be seen in the image at the end.
How to complete the table?Here we have the function:
f(x) = -8
This is a constant function, for every input that we use, the output will be the same one, then:
f(-8) = -8
f(-1) = -8
f(1) = -8
Then the complete table is:
x f(x)
-8 -8
-1 -8
1 -8
And the graph of these 3 points can be seen in the image at the end.
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what is the value of the expression 2x^2-5xy when x =-3 and y=8?
Answer:
156
Step-by-step explanation:
The value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.
Explanation:To find the value of the expression, 2x^2 - 5xy, when x = -3 and y = 8, we just need to substitute the given values into the expression.
So, 2x^2 - 5xy becomes 2*(-3)^2 - 5*(-3)*8 = 2*9 + 15*8 = 18 + 120 = 138
Therefore, the value of the expression 2x^2 - 5xy when x = -3 and y = 8 is 138.
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Step-by-step explanation:
as the description says, the area is a rectangle (8×4) minus the half-circle at the right.
the radius of the (half-)circle is 4/2 = 2, as 4 is the diameter.
the area of the circle is
pi×r² = pi×2² = 4pi
the area of the half-circle is then
4pi/2 = 2pi
the area of the rectangle is
8×4 = 32
the total area is
32 - 2pi = 25.71681469... ≈ 25.7 square units
Answer:
25.7 square units
Step-by-step explanation:
You want the area of a 4 × 8 rectangle with a semicircle of diameter 4 removed from the end.
AreaThe area of the enclosing rectangle is ...
A = LW
A = (8)(4) = 32 . . . . . square units
The are of the missing semicircle is ...
A = 1/2πr² . . . . . . where r is half the diameter
A = 1/2π(4/2)² = 2π ≈ 6.3 . . . . . square units
Then the area of the figure is ...
A = rectangle - semicircle = 32 -6.3 = 25.7 . . . . . square units
The area of the figure is about 25.7 square units.
In a lab experiment, a population of 250 bacteria is able to triple every hour. Which equation matches the number of bacteria in the population after 8 hours?
Answer: 5,250
Step-by-step explanation:
250x3=750
750x7
The radius of container M is 3 inches and the height is 9.5 inches. A cook has
several boxes of sugar that are each the same size and volume. The cook empties 1
box of sugar into container M. He then empties of another box of sugar into
container M to completely fill it. What is the approximate volume, in cubic Inches, of
1 box of sugar?
The volume of container M can be calculated using the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we have:
V = π(3 in)^2(9.5 in)
V ≈ 254.47 cubic inches
Let x be the volume of one box of sugar. According to the problem, the cook emptied one box of sugar into the container, and then added some fraction of another box to completely fill it. This means that the total volume of sugar added is equal to 1 + some fraction of x.
We can set up an equation to solve for x:
1 + (1/n)x = 254.47
where n is the fraction of the second box of sugar added.
Solving for x, we get:
x = (254.47 - 1) n
x = 253.47n
To find the value of n, we can subtract 1 box of sugar from the total volume added, and then divide by the volume of one box:
n = (254.47 - 1) / x
n = 253.47 / x
Substituting the expression for x from above, we get:
n = 253.47 / (253.47n)
n^2 = 253.47 / 1
n ≈ 15.93
Therefore, the volume of one box of sugar is approximately:
x ≈ 253.47 / 15.93
x ≈ 15.91 cubic inches
147 cars were sold during the month of april. 81 had air conditioning and 82 had automatic transmission. 54 had air conditioning only, 55 had automatic transmission only, and 11 had neither of these extras. what is the probability that a randomly selected car had automatic transmission or air conditioning or both?
The Probability that the randomly selected car has either air-conditioning or automatic transmission or both is 0.9252.
The total number of cars sold in April is = 147,
⇒ n(S) = 147,
Let the cars which has Air Conditioning is denoted by "A", and
the number of cars which has automatic transmission be denoted by "B",
the number of cars which has AC = n(A) = 81,
the number of cars which are automatic be = n(B) = 82,
the number of cars which has only AC = n(A∩B') = 54,
the number of cars which are only automatic is = n(A'∩B') = 11,
the number of cars which has neither = n(A'∩B') = 11,
So, the probability that car has neither of these is = 11/147,
We know that, P(A'∩B') = P((A∪B)'),
So, P(A∪B) = 1 - P((A∪B)') = 1 - 11/147 = (147 - 11)/147 = 136/147 = 0.9252,
Therefore, the required probability is 0.9252.
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Can anyone help with this? Sorry about the camera quality
Yes, the ball reach a height of 25 meters from the ground , got the answer by solving equation given .
what is height ?
Height refers to the vertical distance between a point or an object and a reference level, usually the ground or a specific reference point. In the given context, height refers to the vertical distance of the ball from the ground at any given time, as modeled by the function h(t) = -5t² +7t+24.
In the given question,
h(t) = -5t² +7t+24
To find the time it takes for the ball to reach a height of 25 meters, we set h(t) equal to 25 and solve for t:
-5t² + 7t + 24 = 25
Simplifying, we get:
-5t² + 7t - 1 = 0
Using the quadratic formula, we get:
t = (-(7) ± √((7)² - 4(-5)(-1))) / (2(-5))
t = 1.4 seconds or t = 0.143 seconds (rounded to three decimal places)
Therefore, the ball will reach a height of 25 meters after 1.4 seconds or 0.143 seconds.
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QUICK! I need help with this one please
The first term of the polynomial in standard form must be 4y⁴
If Julian wrote the last term as -3x⁴, the terms with the highest degree must have a coefficient of 3.
To get the standard form, we need to combine like terms and arrange the terms in descending order of degree.
The polynomial can be simplified as follows:
4x²y²-2y⁴-8xy³+9x³y+6y⁴-2xy³-3x⁴+x²y²
= -3x⁴ + (4x²y² + x²y²) + (-2y⁴ + 6y⁴) + (-8xy³ - 2xy³) + 9x³y
= -3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y
Therefore, the standard form of the polynomial is
-3x⁴ + 5x²y² + 4y⁴ - 10xy³ + 9x³y
= 4y⁴ + 5x²y² + -3x⁴ - 10xy³ + 9x³y
The term with the highest degree is -3x⁴, and the terms are arranged in descending order of degree. The answer is not one of the options given.
Therefore, the first term of the polynomial in standard form must be 4y⁴.
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i need to identify the value of x that makes each pair of ratios equivalent
1. 2:x and 12:18
2. 5:15 and x:3
3. x:4 and 45:20
4. 21 to x and 7 to 10
5. x to 50 and 16 to 25
6. 6 to 8 and 18 to x
7. 9/36 and x/4
8. 42/22 and 21/x
9. x/7 and 5/1
10. 20/x 4/8
i cant even understand the subject its too hard for me
Answer:
lbozo
Step-by-step explanation:
A seagull is 23 meters above the surface of the ocean. What is its elevation?
Answer: 23 meter
Step-by-step explanation:
meters "above"
elevation means the distance above sea level
amelia started with $54, and spent $6 each day at camp. she has $18 left.write and solve an equation that can be used to find in how many days, d she has left at camp.which equation can be used to determine how many days d she was at camp?
Amelia was at camp for 6 days. The equation used to determine how many days(D) she was at camp is C x D = 6D and S - (C x D) = E
Given data:
S = initial amount = $54
D = the number of days
C = the cost per day = $6
E: the ending amount = $18
Amelia started with S=$54 and spent C=$6 each day at camp.
Therefore, the total amount she spent at camp is given in an algebraic expression that states the product of two variables:
C x D = 6D
Next, she ended with E=$18. So, the equation can be written in algebraic expression that states the difference between the variable:
S - (C x D) = E
Substituting the values in the equation we get:
54 - 6D = 18
54 - 18 = 6D
36 = 6D
D = 6
Therefore, Amelia was at camp for 6 days.
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Your friend just purchased a new sports car for $32,000. he received $6,000 for his trade in and he used that money as a down payment for the new sports car. he financed the vehicle at 6.76% apr over 48 months with a monthly payment of $619.15. determine, from the given information, the finance charge. a. $3,719.20 b. $5,476.10 c. $4,610.64 d. $6,000
The finance charge is $3,723.20, which is closest to option A, $3,719.20.
The total amount of financing that your friend needed for the new sports car was:
$32,000 purchase price - $6,000 trade-in value = $26,000
Your friend financed $26,000 at 6.76% APR over 48 months, with a monthly payment of $619.15.
We can use the monthly payment and the APR to calculate the finance charge over the 48-month period. The finance charge is the difference between the total amount paid (48 months x $619.15 = $29,723.20) and the original amount financed ($26,000).
Finance charge = Total amount paid - Original amount financed
= $29,723.20 - $26,000
= $3,723.20
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Please help quickkkkkkk
2(6×7) + 2(3×7) + 2(3×6)
= 162
a bottle of soap cost 3.45 for 15 ounces. what is the cost per ounce?
Answer:
Step-by-step explanation:
15 divided by 15 is 1
3.45 divided by 15 is 0.23
The cost per ounce is 23 cents, or $0.23
Mr. Sonny's science class is calculating the average number of blinks per minute. Jan blinks 100 times in 5 minutes. What is her blinking rate, in blinks per minute?
find the product of 4x(x+6)
Answer:
4x^2 + 24x.
Step-by-step explanation:
To find the product of 4x(x+6), we can use the distributive property of multiplication.
4x(x+6) = 4x * x + 4x * 6
= 4x^2 + 24x
Answer: 16x
Explanation:
4x(x+6)
4x+12x
16x
Tyler’s fish tank has 12 orange fish and 4 grey fish. What is the ratio of orange fish to Grey fish
Answer:
12:4
=3:1 (Simplified )
Find X in this equation: 5x^2-5x-30=0
x=? x=???
Answer:
x1 = -2;
x2 = 3
Step-by-step explanation:
[tex]5 {x}^{2} - 5x - 30 = 0[/tex]
Solve this quadratic equation (a = 5; b = -5; c = -30)
[tex]d = {b}^{2} - 4ac = ( { - 5})^{2} - 4 \times 5 \times ( - 30) = 25 + 600 = 625 > 0[/tex]
x1 = (-b - √d) / 2a = (5 - 25) / 2 × 5 = -20 / 10 = -2
[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{5 + 25}{2 \times 5} = \frac{30}{10} = 3[/tex]
Determine if each situation is a rotation, a translation, or a reflection
A shape is moved to the right by 5 units. Transformation: Translation
A shape is flipped over a line. Transformation: Reflection
A shape is rotated 90 degrees clockwise. Transformation: Rotation
A shape is moved diagonally to the left and up by 3 units. Transformation: Translation
A shape is reflected over the line y = x. Transformation: Reflection
What is Translation?In geometry, a translation is a type of transformation that moves every point of a figure or an object in a straight line without changing its size, shape, or orientation. It is also referred to as a slide.
To perform a translation, you select a vector (which determines the distance and direction of the movement) and apply it to every point of the figure or object. For example, if you want to translate a shape 4 units to the right and 2 units up, you would add 4 to the x-coordinates of all the points and add 2 to the y-coordinates of all the points.
Situation 1: A shape is moved to the right by 5 units.
Transformation: Translation
Situation 2: A shape is flipped over a line.
Transformation: Reflection
Situation 3 : A shape is rotated 90 degrees clockwise.
Transformation: Rotation
Situation 4 : A shape is moved diagonally to the left and up by 3 units.
Transformation: Translation
Situation 5: A shape is reflected over the line y = x.
Transformation: Reflection
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Complete question:
Determine if each situation is a rotation, a translation, or a reflection.
a survey revealed that 21.5% of the households had no checking account, 66.9% had regular checking accounts, and 11.6% had now accounts. of those households with no checking account 40% had savings accounts. of the households with regular checking accounts 71.6% had a savings account. of the households with now accounts 79.3% had savings accounts. the probability that a randomly selected household has a savings account is:
The probability that a randomly selected household has a savings account is 57.16%. therefore, correct option is (C) 57.16%.
Given,
A survey revealed that 21.5% of the households had no checking account.
Of those households with no checking account, 40% had savings accounts.= 21.5% × 40%= 0.086%66.9%
had regular checking accounts. Of the households with regular checking accounts,
71.6% had a savings account.= 66.9% × 71.6%= 47.8916%11.6% had now accounts.
Of the households with now accounts,
79.3% had savings accounts.= 11.6% × 79.3%= 9.1828%
Therefore, the probability that a randomly selected household has a savings account is:
0.086 + 47.8916 + 9.1828 = 57.16%
So, the correct option is (C) 57.16%.
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The price of a regular snowcone at Icy's Snowcone Stand is $2.85
Find the volume of a regular snowcone.
Find the price per cubic inch of a regular snowcone.
6in and 3in
The volume of a regular snowcone is 56.52 in³.
The price per cubic inch of a regular snowcone is $0.05.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be determined by using this formula:
V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
Volume of cone, V = 1/3 × πr²h
Volume of regular snowcone, V = 1/3 × 3.14 × 3² × 6
Volume of regular snowcone, V = 56.52 in³.
For the price per cubic inch, we have:
Price per cubic inch = Cost/Volume
Price per cubic inch = 2.85/56.52
Price per cubic inch = $0.05
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In the graph shown below, what is f(2)?
A. f(2) = 2
B. f(2) = 1
C. f(2) -1 and f(2) = 2
D. f(2) doesn't exist
Find the length of the hypotenuse of the right triangle. Explain how you can interpret the Pythagorean Theorem using the areas of squares. (photo attached)
Answer:
The length of the hypotenuse is 39. In the step by step explanation I included the Pythagorean Theorem formula and how it converted to the equation here to solve the problem.
Step-by-step explanation:
a² + b² = c²
15² + 36² = 1,521
√1,521 = 39
39 = c
What is the equation of a line parallel to y=-5x+3 that passes through (3,7)