The linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.
What is linear function?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
To determine the linear function that predicts the number of cars sold we need to find the slope of the equation.
The two coordinated given are:
(x1, y1) = (52000, 8980)
(x2, y2) = (57000, 8730)
The slope of the equation is given by:
m = (y2 - y1) / (x2 - x1)
m = (8730 - 8980) / (57000 - 52000)
m = - 0.05
Substituting the value of the coordinates and slope in the point-slope form we have:
y - y1 = m (x - x1)
y - 8980 = -0.05(x - 52000)
y - 8980 = -0.05x + 2600
y = -0.05x + 11580
Hence, the linear function that predicts the number of cars that will be sold at a price of x dollars is y = -0.05x + 11580.
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Which three lengths could be the lengths
of the sides of a triangle?
A. 12 cm, 5 cm, 17 cm
B. 10 cm, 15 cm, 24 cm
C. 9 cm, 22 cm, 11 cm
D. 21 cm, 7 cm, 6 cm
Answer:
A. 12 cm, 5 cm, 17 cm
Step-by-step explanation:
For any three given lengths to be the sides of a triangle, they must satisfy the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each of the options:
A. 12 cm, 5 cm, 17 cm: 5 + 12 = 17, which is greater than 17, so this is a valid triangle.
B. 10 cm, 15 cm, 24 cm: 10 + 15 = 25, which is greater than 24, so this is a valid triangle.
C. 9 cm, 22 cm, 11 cm: 9 + 11 = 20, which is not greater than 22, so this is not a valid triangle.
D. 21 cm, 7 cm, 6 cm: 7 + 6 = 13, which is not greater than 21, so this is not a valid triangle.
Therefore, the three lengths that could be the sides of a triangle are A (12 cm, 5 cm, 17 cm) and B (10 cm, 15 cm, 24 cm).
7. Which of the following graphs would represent the solution set for y ≤ 5?
Height (in inches)
Class Frequency, f
50-52
5
53-55
8
56-58
12
59-61
13
62-64
11
What is the Sum of the Xm'f Coulumn
To find the sum of the Xm'f column, we first need to calculate the midpoint (Xm) for each class interval and then multiply it by the frequency (f) for that interval. The midpoint of each class interval can be calculated as the average of the lower and upper bounds of the interval.
For the first class interval 50-52:
Xm = (50 + 52) / 2 = 51
Xm'f = Xm * f = 51 * 5 = 255
For the second class interval 53-55:
Xm = (53 + 55) / 2 = 54
Xm'f = Xm * f = 54 * 8 = 432
For the third class interval 56-58:
Xm = (56 + 58) / 2 = 57
Xm'f = Xm * f = 57 * 12 = 684
For the fourth class interval 59-61:
Xm = (59 + 61) / 2 = 60
Xm'f = Xm * f = 60 * 13 = 780
For the fifth class interval 62-64:
Xm = (62 + 64) / 2 = 63
Xm'f = Xm * f = 63 * 11 = 693
Finally, we can add up the Xm'f values for each interval to get the sum of the Xm'f column:
Sum of Xm'f = 255 + 432 + 684 + 780 + 693 = 2954
So the sum of the Xm'f column is 2954.
2/23 divided by 3 1/2
Answer:
4/161
Step-by-step explanation:
2×2
____
23×7
=4
161
=4
161
find two numbers with a sum of 13 and a difference of 5
Solve the following proportion:
6/8=8/a
Step-by-step explanation:
Cross multiply to solve for "a":
6 * a = 8 * 8
Simplify the right side:
6 * a = 64
Divide both sides by 6 to isolate "a":
a = 64 / 6
Simplify:
a = 10.67
Please help pic is below
The point (1, 1/2) lie on the equation y(x² + 1) = 1.
What is an ordered pair?An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.
Pair in Order = (x, y)
x is the abscissa, the distance measure of a point from the primary axis x
y is the ordinate, the distance measure of a point from the secondary axis y
Given, A function y(x² + 1) = 1.
y = 1/(x² + 1).
When x = 1, y = 1/2.
When x = - 1, y = 1/2.
So, The points that lie on the equation y(x² + 1) = 1 is (1, 1/2).
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If you buy a phone for $500 and its value decreases by 50% each year, what is it worth
at the end of 2 years?
O $10
$0
O $125
$250
Max’s custom lacrosse stringing experienced fixed costs of $750 and variable costs of $15 for each lacrosse stick that was restrung. Write an equation that can be used to determine the total cost when x sticks are restrung. Then determine the total cost of restringing 32 lacrosse sticks.
The equation representing the total cost is 15x + 750 and the total cost of restringing 32 lacrosse sticks would be $1230.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, The number of lacrosse sticks be 'x' and the total cost is C(x).
Therefore, The equation representing the context is,
C(x) = 25x + 750.
The total cost of restringing 32 lacrosse sticks would be,
C(32) = 15×32 + 750.
C(32) = 480 + 750.
C(32) = 1230.
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1/x+5 + 3/x+4 = -1/x^2+9x+20
Please solve this for me I keep getting -5 as the answer but the answer is no solution.
someone explain.
Thank you
Answer: no solution
Step-by-step explanation:
Write an equation of the line that is parallel to y = 1/2x + 3 and passes through the point (2,-4). A) y = 1/2x-4 - 15 B) y = -2x-4 + 15 C) y = -2x-5 D) y = 1/2x - 5
Answer:
D
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 )
y = [tex]\frac{1}{2}[/tex] x + 3 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute (2, - 4 ) into the partial equation
- 4 = [tex]\frac{1}{2}[/tex] (2) + c = 1 + c ( subtract 1 from both sides )
- 5 = c
y = [tex]\frac{1}{2}[/tex] x - 5 ← equation of parallel line
ANSWER ASAP PLS!
The area of the parallelogram below is ____ square meters
Answer:
Below
Step-by-step explanation:
Area is base ( which is 6 m) times the height ( which is 8m)
6 x 8 = 48 m^2
The life (in hours) of a randomly chosen led light produced by a manufacturer is normally distributed with mean 1100 and standard deviation 70. Find the number of sample if the probability that the mean life is less than 1120 hours is 0.92
The sample size if the probability that the mean life is less than 1120 hours is 0.92 is given as follows:
n = 24.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 1100, \sigma = 70, s = \frac{70}{\sqrt{n}}[/tex]
The p-value of Z when X = 1120 is of 0.92, hence Z = 1.405, and the sample size is obtained as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.405 = \frac{1120 - 1100}{\frac{70}{\sqrt{n}}}[/tex]
[tex]20\sqrt{n} = 70 \times 1.405[/tex]
[tex]n = \left(\frac{70 \times 1.405}{20}\right)^2[/tex]
n = 24.
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Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Is the product positive or negative? Why?
The multiplication expression with eight rational factors are ''positive''.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.
Hence, The multiplication expression with eight rational factors are positive.
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1. You have the digits 0-9. How many 6-digit permutations are odd and do not start with 0
Answer:
We have 10 digits to choose from (0-9), so the total number of 6-digit permutations is 10 × 10 × 10 × 10 × 10 × 10 = 1,000,000.
Of these, the permutations that start with 0 can be eliminated, leaving 9 × 9 × 9 × 9 × 9 × 9 = 729,000.
Now, we need to figure out how many of these are odd. To do this, we note that odd numbers end in 1, 3, 5, 7, or 9. This means that the last digit of an odd 6-digit permutation is always one of these five digits. Since we are choosing the last digit from 5 options, there are 5 × 729,000 = 3,645,000 odd 6-digit permutations that do not start with 0.
The triangles are similar what is the value of x
Answer: 16
Step-by-step explanation:
To get from 3 to 12, you multiply by 4
To get from 5 to 20, you multiply by 4
So you just multiply 4 by 4 to get x
Answer:
x = 16
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{x}{4}[/tex] = [tex]\frac{20}{5}[/tex] = 4 ( multiply both sides by 4 to clear the fraction )
x = 16
The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that
sample of 29 smoke detectors will have a mean lifetime
between 57 and 64 months. Assume that the sample is taken from a large population and the correction factor can be ignored.
Round the final answer to at least four decimal places and intermediate z-value calculations to two decimal places.
The required probability is 0.8945 that a sample of 29 smoke detectors will have a mean lifetime between 57 and 64 months.
To find the probability that a sample mean is between 57 and 64 months, we need to find the standard deviation of the sample mean, which is given by the standard deviation of the population divided by the square root of the sample size.
The standard deviation of the sample mean = standard deviation of the population / square root of sample size = 8 / √(29) = 8 / 5.385 = 1.48
Next, we need to standardize the interval of 57-64 months by subtracting the mean and dividing it by the standard deviation of the sample mean.
z₁ = (57 - 60) / 1.48 = -2.03
z₂ = (64 - 60) / 1.48 = 1.35
Finally, we can use a standard normal table to find the area under the normal curve between z₁ and z₂, which gives us the probability of a sample mean falling in the interval (57, 64).
P(57 < X < 64) = P(-2.03 < Z < 1.35) = 0.9790 - 0.0845 = 0.8945
Therefore, the final answer is 0.8945, rounded to four decimal places.
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1. A biconditional statement says, "A polygon is a square if and only if the polygon has
four equal sides and four right angles." Write the hypothesis and condusion.
2. A statement says, "If the measure of 4] equals the measure of K, the angles are congruent." Write the converse, inverse, and contrapositive of this statement.
3. What is the original statement if the converse of the original statement is "If a number is divisible by two, then it is an even number"? What is the inverse of the original statement?
4. Write the biconditional statement if the hypothesis is "This month is November," and the conclusion is "Next month is December."
5. A right triangle is a triangle that contains a right angle. Write the biconditional statement for the statement above. Also write the converse of the statement. Is the converse a true statement? Explain.
Answer:Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
Step-by-step explanation:
Hypothesis: A polygon has four equal sides and four right angles.
Conclusion: The polygon is a square.
Converse: If the angles are congruent, then the measure of 4] equals the measure of K.
Inverse: If the measure of 4] does not equal the measure of K, then the angles are not congruent.
Contrapositive: If the angles are not congruent, then the measure of 4] does not equal the measure of K.
Original statement: If a number is even, then it is divisible by two.
Inverse: If a number is not divisible by two, then it is not even.
Biconditional statement: This month is November if and only if next month is December.
Biconditional statement: A triangle is a right triangle if and only if it contains a right angle.
Converse: If a triangle contains a right angle, then it is a right triangle.
The converse is not necessarily a true statement as a triangle can contain a right angle and still not be a right triangle (i.e. it may not meet the requirements of all sides being of equal length).
A 2-ft vertical post casts a 10-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. How tall is the cell phone tower in feet? Your answer
The height of the cell phone tower in feet is solved to be 23 feet
How to find the height of the cell phone towerThe height of the cell phone tower is calculated using the concept of similar triangle and the equation is as follows
A 2-ft vertical post casts a 10-in shadow
2 / 10
nearby cell phone tower casts a 115-ft shadow
let the height be x
x / 115
equating the proportions
2 / 10 = x / 115
cross multiplying
10x = 2 * 115
x = 2 * 115 / 10
x = 23 ft
The height of the tower is 23 feet
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Find the difference 800-699
Answer: The answer is 101
11 + 5x < 26 word problem
Answer: x<3
Step-by-step explanation:
Bring the 11 to the other side of the equation, and subtract.
5x<15.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{11 + 5x < 26}[/tex]
[tex]\mathsf{5x + 11 < 26}[/tex]
[tex]\large\textbf{Subtract 11 to both sides:}[/tex]
[tex]\mathsf{5x + 11 - 11 < 26 - 11}[/tex]
[tex]\large\textbf{Simplify it}[/tex]
[tex]\mathsf{5x < 26 - 11}[/tex]
[tex]\mathsf{5x < 15}[/tex]
[tex]\large\textbf{Divide 5 to both sides}[/tex]
[tex]\mathsf{\dfrac{5x}{5} < \dfrac{15}{5}}[/tex]
[tex]\large\textbf{Simplify it}[/tex]
[tex]\mathsf{x < \dfrac{15}{5}}[/tex]
[tex]\mathsf{x < 3}[/tex]
[tex]\large\textbf{You have an \boxed{\rm{\bf o p e n e d}} circle shaded to the left}[/tex]
[tex]\huge\boxed{\mathsf{x < 3}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
In the figure below, there are three right trangles. Complete the following. (Please answer quickly if possible!)
The similarity statement is competed as follows
triangle LMJ is similar to triangle LMK is similar to LKJThe proportion is completed as below
KL / KJ = ML / KLLJ / MJ = KJ / LJWhat are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
KL / KJ and ML / KL
LJ / MJ and KJ / LJ
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plot the numbers -1.5 3/2, 3/2 and-4/3 on the number line.
Answer: -1.5, -4/3, 3/2, 3/2
Step-by-step explanation:
First, convert the numbers to decimals or fractions.
-1.5
3/2 = 1.5
3/2 = 1.5
-4/3 = -1.3
Therefore, on a number line, the numbers would be in the following order:
-1.5, -4/3, 3/2, 3/2
Sean’s baby brother sleeps about
13 hours a day. If he takes
2 two-hour naps, how long does
he sleep at night?
Answer:
He sleeps about 9 hours at night.
Step-by-step explanation:
If Sean's baby brother sleeps 13 hours a day, and takes 2 two-hour naps during the day, he sleeps 2 * 2 = 4 hours during the day.
SOOO, he sleeps 13 - 4 = 9 hours at night.
classafy the numbers some numbers are more than 1 box numbers are 54,72,84,90,96 sections are divisible by 5 and 9 divisible by 6 and 9 divisable by 2 and 6
If f(x)=2x-10 and the domain of f(x) is the set of untethers from -1 to 3 which values are elements of the range of f(x) Select all that apply
Answer:The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2
Step-by-step explanation:
Write your own expression with coefficient -4 and constant 8.
Answer: you need to do it on your own
Step-by-step explanation:
Mr. Olsen has a computer business in which he sells everything at 44.5% above the wholesale price. If he purchased a printer for $80 wholesale, what will be the retail price?
If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Mr. Olsen has a PC business wherein he sells everything at 44.5% above the wholesale price. On the off chance that he bought a printer for $80 wholesale.
Then the retail price is given as,
⇒ $80 x (1 + 0.445)
⇒ $80 x 1.445
⇒ $115.60
If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.
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Find the surface area if the pyramid
Answer: [tex]533 yd^{2}[/tex]
Step-by-step explanation:
The surface area of the base is:
(20 x 17.3) / 2
= 346 / 2
= 173
The surface area of one of the three identical triangles is:
(20 x 12) / 2
= 240 / 2
= 120
So in total, your answer would be one base plus three of those identical triangles:
173 + (3 x 120)
= [tex]533 yd^{2}[/tex]
The boiling point of water is 212°F at sea level. Andres lives at an elevation of
7500 ft and finds that water boils at 198°F, What is the percent decrease in
the boiling point of water from sea level to 7,500 ft? Give your answer to the
nearest tenth of a percent. Show your work.
The percent decrease in the boiling point of water from sea level to 7,500 feet is equal to 18.7%.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to determine the percent decrease in the boiling point of water from sea level to 7,500 feet, we would determine the difference in temperature as follows;
Difference in temperature = 212°F - 198°F
Difference in temperature = 14°F
Percentage decrease = 14/7500 × 100
Percentage decrease = 0.00187 × 100
Percentage decrease = 18.7%.
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