Final answer:
To determine when the number of new cars reaches 15,000, the quadratic equation 26t^2 + 168t + 4208 = 15,000 is solved for t and then added to 1958.
Explanation:
To find the year when the number of new cars reaches 15,000, we need to set the equation C = 26t^2 + 168t + 4208 equal to 15,000 and solve for t, where t is the number of years since 1958.
First, set up the equation: 15,000 = 26t^2 + 168t + 4208.
To solve for t, we subtract 15,000 from both sides to get the quadratic equation: 0 = 26t^2 + 168t - 10,792.
Next, we use the quadratic formula [tex]t = (-b \pm \sqrt{b^2 - 4ac}) / (2a)[/tex], where a = 26, b = 168, and c = -10,792.
Plugging the values into the quadratic formula, we get the two possible solutions for t. After calculating the roots, we discard any negative value as it would not make sense in the context of time since 1958. The positive year will give us the answer we need.
Adding the positive value of t to 1958, we obtain the year in which the number of new cars purchased will reach 15,000.
A farmer owns pigs, chickens, and ducks. When all her animals are together, she has 30 feathered animals, and the animals all together have a total of 120 legs and 90 eyes. (All the animals have the expected number of parts.) How many of each animal might she have?
She has 18 pigs, 13 chickens, and 17 ducks.
She has 10 pigs, 15 chickens, and 15 ducks.
She has 15 pigs, 12 chickens, and 18 ducks.
She has 12 pigs, 15 chickens, and 15 ducks.
To solve this problem, let us first assign some variables. Let us say that:
x = pigs
y = chickens
z = ducks
From the problem statement, we can formulate the following equations:
1. y + z = 30 ---> only chicken and ducks have feathers
2. 4 x + 2 y + 2 z = 120 ---> pig has 4 feet, while chicken and duck has 2 each
3. 2 x + 2 y + 2 z = 90 ---> each animal has 2 eyes only
Rewriting equation 1 in terms of y:
y = 30 – z
Plugging this in equation 2:
4 x + 2 (30 – z) + 2 z = 120
4 x + 60 – 2z + 2z = 120
4 x = 120 – 60
4 x = 60
x = 15
From the given choices, only one choice has 15 pigs. Therefore the answers are:
She has 15 pigs, 12 chickens, and 18 ducks.
What is 784 in expanded form, using exponents?
If two sides of a triangle are 12 and 17, and the included angle is 60, what is the area of the triangle
Three cards are drawn with replacement from a standard deck. what is the probability that the first card will be a diamond, the second card will be a black card, and the third card will be an ace? express your answer as a fraction or a decimal number rounded to four decimal places.
there are 13 diamonds per deck
26 black cards
4 aces
so a 13/52 chance for a diamond
a 26/52, reduced to 1/2 chance for a black card
and a 4/52 chance for an ace
13/52 x 1/2 x 4/52 = 52/5408 = 1/104 probability
Use the three steps to solve the problem. the length of a rectangle is 2 inches less than 3 times the number of inches in its width. if the perimeter of the rectangle is 28 inches, what is the width and length of the rectangle?
Solve by the linear combination method (with or without multiplication). x + y = 40 0.08x + 0.03y = 1.7
Answer:
-_- Answer is -3
Step-by-step explanation:
Doing the instruction vidio.
The endpoints of segment AC are A( – 7, – 3) and C( 8, 4). Point B is somewhere in between AC. Determine the coordinates of point B if the ratio of the distances between these points is AB : BC = 5 : 2.
Suppose a laboratory has a 30 g sample of polonium-210. The half-life of polonium-210 is about 138 days. How many half-lives of polonium-210 occur in 1104 days? How much polonium is in the sample 1104 days later?
Answer:
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
Step-by-step explanation:
Initial mass of the polonium-210 = 30 g
Half life of the sample, = [tex]t_{\frac{1}{2}}=138 days[/tex]
Formula used :
[tex]N=N_o\times e^{-\lambda t}\\\\\lambda =\frac{0.693}{t_{\frac{1}{2}}}[/tex]
where,
[tex]N_o[/tex] = initial mass of isotope
N = mass of the parent isotope left after the time, (t)
[tex]t_{\frac{1}{2}}[/tex] = half life of the isotope
[tex]\lambda[/tex] = rate constant
[tex]\lambda =\frac{0.693}{138 days}=0.005021 day^{-1}[/tex]
time ,t = 1104 dyas
[tex]N=N_o\times e^{-(\lambda )\times t}[/tex]
Now put all the given values in this formula, we get
[tex]N=30g\times e^{-0.005021 day^{-1}\times 1104 days}[/tex]
[tex]N=0.1174 g[/tex]
Number of half-lives:
[tex]N=\frac{N_o}{2^n}[/tex]
n = Number of half lives elapsed
[tex]0.1174 g=\frac{30 g}{2^n}[/tex]
[tex]n = 7.99\approx 8[/tex]
8 half-lives of polonium-210 occur in 1104 days.
0.1174 g of polonium-210 will remain in the sample after 1104 days.
How to solve this? Please help!
Which of the following polynomials corresponds to the subtraction of the multivariate polynomials 19x^3+44x^2y+17 and y^3-11xy^2+2x^2y-13x^3
A. y^3-6x^3+33x^2y+2x^2y+17
B. 20x^3-y^3+33x^2y+2x^2y+17
C. 31x^3-6x^3+44x^2y+11x^2y+17
D. 32x^3-y^3+42x^2y+11x^2y+17
On the day their child was born, her parents deposited $25,000 in a savings account that earns 11% interest annually. How much is in the account the day the child turns 16 years old (rounded to the nearest cent)? Hint: an = a1(1 + r)n, r ≠ 1, where a1 is the initial amount deposited and r is the common ratio or interest rate.
Answer choices:
$119,614.74 $132,772.36 $128,612.52 $440,000.00
Final answer:
After using the compound interest formula with an initial deposit of $25,000, an annual interest rate of 11%, and a time period of 16 years, the balance rounds to $120,034.10, which does not match any of the provided answer choices.
Explanation:
To find out how much is in the account when the child turns 16 years old, we can use the formula for compound interest: an = a1(1 + r)n, where a1 is the original amount deposited, r is the annual interest rate (expressed as a decimal), and n is the number of years the money is invested. In this case, a1 is $25,000, r is 0.11 (11%), and n is 16.
Using the formula, we calculate the account balance as follows:
Account Balance = 25,000(1 + 0.11)16
Account Balance = 25,000(1.11)16
Account Balance = 25,000(4.801364)
Account Balance = $119,999.10
However, this result is not in the given answer choices, so let's ensure we are rounding to the nearest cent:
Account Balance = $120,034.09 (before rounding)
Account Balance = $120,034.10 (after rounding to the nearest cent)
None of the answer choices matches this amount, so it is possible there has been a mistake in the provided choices or in our calculations. We should double-check the interest rate, time period, and the formula used.
evaluate 9 + 11g - 4h when g = 2 and h = 7
Simplify this using the imaginary i
If x and y are two nonnegative numbers and the sum of twice the first ( x ) and three times the second ( y ) is 60, find x so that the product of the first and cube of the second is a maximum.
To find the value of x such that the product of the first number and the cube of the second number is a maximum, we need to solve the equations and find the critical points. From the critical points, we can determine the maximum value of the product.
Explanation:To find the value of x such that the product of the first number and the cube of the second number is a maximum, we need to use the given condition that the sum of twice the first number and three times the second number is 60. Let's solve this step-by-step.
Let the first number be x and the second number be y.According to the given condition, 2x + 3y = 60.We need to maximize the product xy^3.To maximize the product, we can use the method of substitution.From step 2, we have 2x = 60 - 3y.Substituting the value of 2x from step 5 into the product xy^3, we get (60 - 3y)y^3.To find the maximum value, we need to find the critical points, which are the points where the derivative is equal to zero or does not exist.Find the derivative of (60 - 3y)y^3, which is -9y^2 + 180y - 3y^4.Set the derivative equal to zero and solve for y.From the values of y, find the corresponding values of x using the equation 2x = 60 - 3y.Compare the values of xy^3 for different y values to find the maximum.Learn more about Maximum Product here:https://brainly.com/question/35486509
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Evaluate 4x - 7 when x = 6
Replace the variables/letters in the expression above with the values assigned to them, so replace all x’s with 6 in this example
implify the expression (following order of operations)
When [tex]\(x = 6\)[/tex], the expression [tex]\(4x - 7\)[/tex] simplifies to 17 following the order of operations.
To evaluate the expression [tex]\(4x - 7\)[/tex] when [tex]\(x = 6\)[/tex], substitute the value of [tex]\(x\)[/tex] into the expression and simplify using the order of operations.
[tex]\[4x - 7\][/tex]
Replace [tex]\(x\)[/tex] with 6:
[tex]\[4(6) - 7\][/tex]
Following the order of operations (PEMDAS), perform the multiplication first:
[tex]\[24 - 7\][/tex]
Now, perform the subtraction:
[tex]\[17\][/tex]
Thus, when \(x = 6\), the value of [tex]\(4x - 7\)[/tex] is 17.
In this expression, the variable [tex]\(x\)[/tex] is multiplied by 4, and then 7 is subtracted from the result. By substituting the value of [tex]\(x\)[/tex], which is 6 in this case, and simplifying according to the order of operations, we obtain the final result of 17.
Mentally estimate the total cost of items that have the following prices $1.85 $.98 $3.94 $9.78 and $6.18 round off the answer to the nearest half dollar
A. $22.50
B. $22.59
C. $23.00
D. $22.30
the first 4 would be rounded up tot he nearest dollar and the last one rounded down to the nearest dollar
doing that I estimate $23.00
Answer is C
The temperature dropped 2° F every hour for 6 hours. What was the total number of degrees the temperature changed in the 6 hours
When the reciprocal of three times a number is subtracted from 7, the result is the reciprocal of twice the number. find the number?
To find the number, we set up the equation 7 - 1/(3x) = 1/(2x) and solve for x.
Explanation:To find the number, we need to set up an equation based on the given information.
Let's assume the number is 'x'.
According to the problem, the reciprocal of three times the number is subtracted from 7 and is equal to the reciprocal of twice the number. We can write this as:
7 - 1/(3x) = 1/(2x)
To solve this equation, we can multiply both sides by the common denominator, which is 6x. This will eliminate the fractions.
6x * 7 - 6x * 1/(3x) = 6x * 1/(2x)
42x - 2 = 3
Subtracting 2 from both sides, we get:
42x = 1
Dividing both sides by 42, we find:
x = 1/42
Therefore, the number is 1/42.
A construction crew wants to hoist a heavy beam so that it is standing up straight. ey tie a rope to the beam, secure the base, and pull the rope through a pulley to raise one end of the beam from the ground. When the beam makes an angle of 408 with the ground, the top of the beam is 8 ft above the ground. e construction site has some telephone wires crossing it. e workers are concerned that the beam may hit the wires. When the beam makes an angle of 608 with the ground, the wires are 2 ft above the top of the beam. Will the beam clear the wires on its way to standing up straight? Explain.
Using trigonometry, it can be determined that the beam will clear the wires when it stands up straight. The beam's length remains constant and by finding the height of the beam at different angles, we can confirm that it will not hit the wires.
Explanation:The problem can be solved using trigonometry. Firstly, you need to find out the length of the beam when it makes an 40° angle with the ground. The length of the beam would be 8 ft / sin(40°) around 12.61 ft. Now, when the beam makes a 60° angle with the ground, the top of the beam will be sin(60°) * 12.61 ft = 10.92 ft off the ground. Because the wires are 2 ft above that (at 8 ft + 2 ft = 10 ft), the beam will clear the wires as it stands up straight.
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By applying trigonometry principles, it is determined that the beam will not clear the wires when it is lifted to stand up straight as the top of the beam at 60° angle is lower than the bottom of the wires.
Explanation:To answer whether the beam will clear the wires when it is lifted, we need to apply basic trigonometry principles. First, we determine the height of the beam when it is at a 40° angle with the ground, and we know the top is 8 ft above the ground. We can use the tangent of the angle to relate this height to the length of the beam, which remains constant as the beam is raised.
So we have tan(40°) = 8ft/beam_length. Solving for beam_length, we get beam_length = 8ft/tan(40°) ≈ 9.442ft.
Next, when the beam makes a 60° angle with the ground, it is not fully raised and the wires are 2ft above the beam's top. The length of the beam when it's at this angle is beam_length = 2ft + height_at_60°. We can use the tangent function again to find this height, which gives us tan(60°) = height_at_60°/beam_length.
Solving for height_at_60°, we get height_at_60° = beam_length * tan(60°), substituting beam_length from earlier, height_at_60° = 9.442ft * tan(60°) ≈ 16.34ft.
As the bottom 2 ft of the wires are not cleared by the 16.34 ft high beam, the conclusion is that the beam will not clear the wires when it is being erected up straight.
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Create a factorable polynomial with a GCF of 2y. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
I already made my polynomial, 4y^1 + 6y^3
I just don't understand how to get two equivalent forms(please explain if you can)
What is the factorization of the polynomial graphed below? Assume it has no constant factor.
A. x(x+2)
B. (x-2)(x-2)
C. x(x-2)
D. (x+2)(x+2)
Answer:
Option: B is correct.
The factorization of the polynomial graphed below is:
f(x)=(x-2)(x-2)
Step-by-step solution:
Clearly from the graph we could see that the graph of the function touches x=2.
that means that x=2 is a root of the function
Also when the graph touches the point of x-axis and does not pass that point than that zero is the repeated zero of the function.
That means that x=2 is a repeated zero of the function f(x).
Hence,
The factorization of the polynomial graphed below is:
f(x)=(x-2)(x-2)
Hence, option B is correct.
( Also in first option:
A) x(x+2)
x=0 must also be an zero but in the graph we could see that x=0 is not a solution.
Hence option A is false.
C)
x(x-2)
again as in option: A x=0 must be a solution.
Hence, option C is false.
D)
(x+2)(x+2)
x=-2 must be a solution but the graph does not touches x=-2.
Hence, option D is incorrect )
What are the real zeros of x^3 + 4x^2 − 9x − 36
Answer:
x = −3, 3, −4
Step-by-step explanation:
Which equation results from isolating a radical term and squaring both sides of the equation for the equation sqrt(c-2) - sqrt(c) = 5
A) c-2=25+c
B) c-2=25-c
C) c-2 = 25+c-10sqrt(c)
D) c-2 = 25-c+10sqrt(c)
Answer:
D) c - 2 = 25 + c + 10√c
Step-by-step explanation:
The given equation is sqrt(c-2) - sqrt(c) = 5
Taking square on both sides, we get
Here we used ( a+ b)^2 = a^2 + b^2 + 2ab formula.
c - 2 = 5^2 + (√c)^2 + 2(5)√c
c - 2 = 25 + c +10√c
Hope this helps!! Have a great day!! ❤
The correct equation resulting from isolating a radical term and squaring both sides of the original equation is D) [tex]\( c-2 = 25-c+10\sqrt{c} \)[/tex].
To arrive at this result, let's start with the original equation and isolate one of the radical terms:
[tex]\[ \sqrt{c-2} - \sqrt{c} = 5 \][/tex]
Now, isolate the radical on one side:
[tex]\[ \sqrt{c-2} = 5 + \sqrt{c} \][/tex]
Next, square both sides to eliminate the radical:
[tex]\[ (\sqrt{c-2})^2 = (5 + \sqrt{c})^2 \] \[ c-2 = 25 + 2 \cdot 5 \cdot \sqrt{c} + (\sqrt{c})^2 \] \[ c-2 = 25 + 10\sqrt{c} + c \][/tex]
Now, we want to isolate the term with the radical on one side and the rest on the other side:
[tex]\[ c-2 = 25 + 10\sqrt{c} + c \][/tex]
Subtract c from both sides to get:
[tex]\[ c-2-c = 25 + 10\sqrt{c} \] \[ -2 = 25 + 10\sqrt{c} \][/tex]
Finally, add 2 to both sides to isolate the radical term:
[tex]\[ -2 + 2 = 25 + 10\sqrt{c} + 2 \] \[ 0 = 25 + 10\sqrt{c} - 2 \] \[ c-2 = 25 - c + 10\sqrt{c} \][/tex]
This matches option D, confirming that the correct equation is:
[tex]\[ c-2 = 25-c+10\sqrt{c} \][/tex]
Determine if the function is one-to-one. A decreasing line intercepting the y axis at 0, 5.
During a period of 11 years 737737 of the people selected for grand jury duty were sampled, and 6868% of them were immigrants. use the sample data to construct a 99% confidence interval estimate of the proportion of grand jury members who were immigrants. given that among the people eligible for jury duty, 69.469.4% of them were immigrants, does it appear that the jury selection process was somehow biased against immigrants?
How many unique ways are there to arrange the letters in the word APE
The number of unique ways that are there to arrange the letters in the word APE is 6 ways
Factorial experimentFrom the question, we are to determine the number of ways the word APE can be arranged.
Since there are 3 letters in the word APE, the number of ways it can be arranged is expressed as:
3! = 3 * 2 * 1
3! = 6 ways
Hence the number of unique ways that are there to arrange the letters in the word APE is 6 ways
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A rectangular table top has a perimeter of 24 inches and an area of 35 square inches. find its dimensions.
The value of dimensions of rectangle are 5 and 7.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
A rectangular table top has a perimeter of 24 inches and an area of 35 square inches.
Let the dimensions of rectangle are;
Length = L
Width = W
So, We can formulate;
⇒ 2 ( L + W ) = 24
⇒ L + W = 12 ..(i)
And,
⇒ L × W = 35
⇒ L = 35 / W ... (ii)
Substitute the value from (ii) in (i), we get;
⇒ L + W = 12
⇒ 35/W + W = 12
⇒ 35 + W² = 12W
⇒ W² - 12W + 35 = 0
⇒ W² - (7W + 5W) + 35 = 0
⇒ W² - 7W - 5W + 35 = 0
⇒ W (W - 7) - 5 (W - 7) = 0
⇒ (W - 5) (W - 7) = 0
⇒ W = 5
And, W = 7
And, We get;
⇒ L = 35 / W
Put W = 5;
⇒ L = 35 / 5
⇒ L = 7
And,
⇒ L = 35 / W
Put W = 7;
⇒ L = 35 / 7
⇒ L = 5
Thus, The possible values of dimensions are;
⇒ 5 and 7.
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How will the perimeter of the rectangle change if each side is increased by a factor of 10? the long side has 6cm and the short side is 3cm.
a.The perimeter will be 1/10 the original.
b.The perimeter will be 1/100 the original
c.The perimeter will be 10 times the original.
d.The perimeter will be 100 times the original.
Answer: Option 'C' is correct.
The perimeter will be 10 times the original .
Step-by-step explanation:
Since we have given that
Length of the rectangle = 6 cm
Breadth of the rectangle = 3 cm
As we know the formula for "Perimeter of rectangle "
[tex]\text{Perimeter of original rectangle }=2(Length+ Breadth)\\\\\text{Preimeter of rectangle }=2(6+3)\\\\\text{Perimeter of rectangle }=18\ cm[/tex]
According to question, each side is increased by a factor of 10
so, Perimeter of new rectangle is given by
[tex]10\times 2\times (6+3)\\\\=180\ cm[/tex]
Hence, Option 'C' is correct.
So, the perimeter will be 10 times the original .
Describe the transformation of the graph of f into the graph of g as either a horizontal or vertical stretch. f(x)=sqrt(x) and g(x)=sqrt(0.5x)
The transformation of the function f(x) to g(x) is a horizontal stretch.
Step-by-step explanation:The parent function f(x) is given by:
[tex]f(x)=\sqrt{x}[/tex]
and the transformed function g(x) is given by:
[tex]g(x)=\sqrt{0.5x}[/tex]
Now we know that the transformation of the type:
f(x) → f(bx)
is a horizontal stretch if 0<b<1
and is a horizontal shrink if b>1
Here we have:
[tex]b=\dfrac{1}{2}=0.5[/tex]
i.e.
[tex]0<b<1[/tex]
This means that the transformation of the function f(x) to g(x) is a horizontal stretch by a factor of 2.
An object is thrown upward from the top of an 80ft tower.
The height h of the object after t seconds is represented by the quadratic equation h= -16t^2 + 64t + 80.
After how many seconds will the object hit the ground?
A. 29 seconds
B. 6.4 seconds
C. 5.0 seconds
D. 8.0 seconds