Answer:
To write the polynomial function m(x) = x + x^2 - 1 in standard form, we rearrange the terms in descending order of degree:
m(x) = x^2 + x - 1
Polynomial name: Quadratic polynomial
Degree: 2 (the highest exponent is 2)
Leading coefficient: 1 (the coefficient of the highest-degree term)
Constant term: -1 (the term without any variable)
Question 5 (1 point)
For the following observations: 2, 5, 3, 2, 4, 6, 2, 4, the mode equals
1) 2
2) 3
3) 4
4) none of the other answers
The mode of the given observations 2, 5, 3, 2, 4, 6, 2, 4 is 2, so the correct answer is 1) 2.
To find the mode of a set of observations, we need to identify the value that appears most frequently.
Let's analyze the given observations: 2, 5, 3, 2, 4, 6, 2, 4.
Looking at the observations, we can see that the number 2 appears three times, while the numbers 5, 3, 4, and 6 appear only once each.
Since the number 2 appears more frequently than any other number in the set, the mode of these observations is 2.
Therefore, the correct answer is 1) 2.
The mode is a measure of central tendency that represents the most commonly occurring value in a data set.
It can be useful in identifying the most frequent value or category in a dataset.
In this case, the mode of the given observations is 2 because it appears more frequently than any other number.
It's important to note that a dataset can have multiple modes if there are two or more values that occur with the same highest frequency. However, in this specific case, the number 2 is the only value that appears more than once, making it the mode.
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5. A person observes that from point A, the angle of elevation to the top of a cliff at D is 30°. Another person at point B, notes that the angle of elevation to the top of the
cliff is 45°. If the height of the cliff is 80.0 m, find the distance between A and B. Show the steps of your solution.
Answer:
In a 30°-60°-90° triangle, the length of the longer leg is √3 times the length of the shorter leg. So AC = 80√3.
In a 45°-45°-90° triangle, both legs are congruent. So BC = 80.
AB = AC - BC = (80√3 - 80) meters
= 80(√3 - 1) meters
= about 58.56 meters
The distance between points A and B is approximately 138.6 meters.
To find the distance between points A and B, we can use the concept of trigonometry and the given information.
Let's denote the distance between points A and B as x.
From point A, the angle of elevation to the top of the cliff at point D is 30°. This means that in the right triangle formed by points A, D, and the top of the cliff, the opposite side is the height of the cliff (80.0 m) and the adjacent side is x. We can use the tangent function to calculate the length of the adjacent side:
tan(30°) = opposite/adjacent
tan(30°) = 80.0/x
Simplifying the equation, we have:
x = 80.0 / tan(30°)
Using a calculator, we can find the value of tan(30°) ≈ 0.5774.
Substituting the value, we get:
x = 80.0 / 0.5774
Calculating the value, we find:
x ≈ 138.6 meters
In light of this, the separation between positions A and B is roughly 138.6 metres.
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Divide. (4x^3− 12x + 11) ÷ (2x − 2)
How much is 700000 in Penny’s
Answer:
$7000
Step-by-step explanation:
700,000 dollars is equal to 70,000,000 pennies.
To convert 700,000 to pennies.
We need to multiply the number by 100, since there are 100 pennies in a dollar.
1 dollar = 100 pennies.
So, 700,000 × 100
= 70,000,000
Therefore, 700,000 is equal to 70,000,000 pennies.
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Please help me with this question
Answer:
try (gauth math) could be helpful take screen shot and upload it it may be there or not hopefully it is
The pyramid and prism above have the same triangular base and height. The volume of the pyramid is 18 cubic inches. What is the volume of the prism?
A. 36 cubic inches
B. 72 cubic inches
C. 6 cubic inches
D. 54 cubic inches
Will give Branliest Hurry!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Which linear graph represents a proportional relationship? a graph of a line that passes through the points 0 comma 0 and 2 comma negative 1 a graph of a line that passes through the points 0 comma 1 and 1 comma 3 a graph of a line that passes through the points 0 comma 3 and 1 comma 3 a graph of a line that passes through the points 0 comma negative 1 and negative 1 comma 2
Answer:On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).
Step-by-step explanation:
If sin 0=8/17, and tan0<0, what is cos(0)
Use exact values. No decimals.
(0 means theta)
Answer:
Given that sin(θ) = 8/17 and tan(θ) < 0, we can use the trigonometric identity to find cos(θ).
Since sin(θ) = opposite/hypotenuse, we can assign a value of 8 to the opposite side and a value of 17 to the hypotenuse.
Let's assume that θ is an angle in the second quadrant, where sin(θ) is positive and tan(θ) is negative.
In the second quadrant, the x-coordinate (adjacent side) is negative, and the y-coordinate (opposite side) is positive.
Using the Pythagorean theorem, we can find the length of the adjacent side:
adjacent^2 = hypotenuse^2 - opposite^2
adjacent^2 = 17^2 - 8^2
adjacent^2 = 289 - 64
adjacent^2 = 225
adjacent = √225
adjacent = 15
Therefore, the length of the adjacent side is 15.
Now we can calculate cos(θ) using the ratio of adjacent/hypotenuse:
cos(θ) = adjacent/hypotenuse
cos(θ) = 15/17
So, cos(θ) = 15/17.
Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
J
Answer:
I wish you good luck in finding your answer
Answer: 115
Step-by-step explanation:
Given that P(A)=0.450 and P(B)=0.680 and P( A U B)=0.824. Find the probability
The probability of the union of events A and B, P(A U B), is 0.824.
To find the probability, we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
Given that P(A) = 0.450, P(B) = 0.680, and P(A U B) = 0.824, we can substitute these values into the formula:
0.824 = 0.450 + 0.680 - P(A ∩ B)
To find the probability of the intersection of events A and B (P(A ∩ B)), we rearrange the equation:
P(A ∩ B) = 0.450 + 0.680 - 0.824
P(A ∩ B) = 1.130 - 0.824
P(A ∩ B) = 0.306
Therefore, the probability of the intersection of events A and B, P(A ∩ B), is 0.306.
We can also calculate the probability of the union of events A and B, P(A U B), by substituting the given values into the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.450 + 0.680 - 0.306
P(A U B) = 0.824
Therefore, the probability of the union of events A and B, P(A U B), is 0.824.
In summary, we have found that the probability of the intersection of events A and B, P(A ∩ B), is 0.306, and the probability of the union of events A and B, P(A U B), is 0.824, based on the given probabilities.
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Write the inequality and solve.
Negative nine times one more than a number is not as much as twelve times that number plus nine.
Answer:
-9(x+1) < 12x+9
if you need me to solve it here it is:
-9x - 9 < 12x + 9
+ 9 +9
-9x < 12x + 18
-12x -12x
-18x < 18
(divide by -18 on both sides)
x < - 1
Therefore, any number is that is greater than -1 will work for this inequality.
Hope this helps!
Use the LinReg(ax+b) function in the calculator to determine the regression line for the following data:
X 14.56 13.58 12.69 14.87 15.68 14.28
Y 0.25 0.84 0.71 0.65 0.35 0.61
Your answers should be numerical values rounded to four decimal places.
The regression line is y =
Check
x+
The regression line is y = -0.1471x + 2.2386.
To determine the regression line using the LinReg(ax+b) function, we input the given data into the calculator and obtain the values for a and b in the regression equation.
Using the LinReg(ax+b) function with the given data, we have:
X: {14.56, 13.58, 12.69, 14.87, 15.68, 14.28}
Y: {0.25, 0.84, 0.71, 0.65, 0.35, 0.61}
After performing the regression analysis, we obtain the regression equation as follows:
y = -0.2012x + 3.4986
Therefore, the regression line is y = -0.2012x + 3.4986.
Please note that the numerical values provided for a and b are rounded to four decimal places for simplicity.
To check the regression line, we can substitute the given x-values into the equation and compare the calculated y-values with the actual y-values to verify the accuracy of the regression line.
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4
cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a diamond? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer:
[tex] \frac{1}{4} [/tex]
Answer:
the probability that at least one of the cards drawn is a diamond is 5/32
Step-by-step explanation:
In a standard 52-card deck, there are 13 diamond cards,
Now,
The probability of a card being a diamond is ,
P = 13/52
P = 1/4
Now, we have to find the probability that atleast one of the 4 cards is a diamond, we calculate the probabilities,
There is 1 diamond in the 4 cards,
Hence the other 3 are not diamonds i.e the porbability for not being a diamond is,
N = 1-1/4 = 3/4
So,
The total probability is,
T1 = (3/4)(3/4)(3/4)(1/4)
T1 = 27/256
There are 2 diamonds in the 4 cards,
And the other 2 are not diamonds, we get,
T2 = (1/4)(1/4)(3/4)(3/4)
T2=9/256
There are 3 diamonds in the 4 cards,
and 1 is not,
T3 = (1/4)(1/4)(1/4)(3/4)
T3 = 3/256
ALL FOUR are diamonds,
T4 = (1/4)(1/4)(1/4)(1/4)
T4 = 1/256
Hence, the probability that at least 1 is a diamond is,
T = T1 + T2 + T3 + T4
T = (27/256) + (9/256) + (3/256) + (1/256)
T = 40/256
T = 5/32
Find the measure of the numbered angles
Look at picture for reference
Show work when possible
The measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.
What is the measure of the numbered angles?The measure of the numbered angles is calculated by applying the following formula as follows;
Rhombus has equal sides and equal angles.
angle 2 = angle 57⁰ (alternate angles are equal)
angle 1 = 90⁰ (diagonals of rhombus intersects each other at 90⁰)
angle 3 = angle 4 (base angles of Isosceles triangle )
angle 3 = angle 4 = ¹/₂ x 90⁰
angle 3 = angle 4 = 45⁰
Thus, the measure of the numbered angles in the rhombus is determined as angle 1 = 90⁰, angle 2 = 57⁰, angle 3 = 45⁰, and angle 4 = 45⁰.
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A gravel company charges a fee for a load of gravel Plus a charge for each mile from
the gravel pit to the final destination of the load. Let x represent the number of
miles to the destination and y
represent the total cost of the load. The charge to deliver a load 40 miles is $280
and the charge to deliver a load 56 miles is $292.
Find the slope.
1) 16
2) 7
3) 0.75
4) 21.3
5) 5.21
The slope of 0.75 corresponds to option 3. So, the correct answer is 3) 0.75.
To find the slope, we can use the formula for the slope of a line:
slope (m) = (change in y) / (change in x)
In this case, x represents the number of miles to the destination and y represents the total cost of the load.
Given that the charge to deliver a load 40 miles is $280 and the charge to deliver a load 56 miles is $292, we can set up two points on the line: (40, 280) and (56, 292).
Now let's calculate the change in y and change in x:
Change in y = 292 - 280 = 12
Change in x = 56 - 40 = 16
Plugging these values into the slope formula:
slope (m) = (change in y) / (change in x) = 12 / 16 = 0.75
Therefore, the slope of the line representing the relationship between the number of miles (x) and the total cost of the load (y) is 0.75.
Option 3 is correct.
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amar is a unmarried newly secondary class joint secretary of minister of finance. his monthly salary with dearness allowance is Rs 58,786. he gets one month salary for expense of festival at once. 10% of his monthly salary deposited in employee's provident fund (EPF) and Rs 3,300 in life insurance in each month.the government deposits the same EPF amount in the fund
1) find his yearly income assessable income
2) find taxable income of amar
3) how much income tax does he pay in total? find it
The correct answer is Yearly income assessable income: Rs 7,75,974
Taxable income of Amar: Rs 7,66,796
To find Amar's yearly income, we'll consider his monthly salary and additional benefits:
Yearly Income:
Monthly salary = Rs 58,786
Yearly salary = Monthly salary * 12 = Rs 58,786 * 12 = Rs 7,05,432
Additional benefits:
One month salary for festival expense = Rs 58,786
EPF contribution per month (deducted from salary) = 10% of monthly salary = 0.10 * Rs 58,786 = Rs 5,878
Government's EPF contribution = Rs 5,878
Total additional benefits per year = One month salary + EPF contribution + Government's EPF contribution = Rs 58,786 + Rs 5,878 + Rs 5,878 = Rs 70,542
Yearly income assessable income = Yearly salary + Total additional benefits = Rs 7,05,432 + Rs 70,542 = Rs 7,75,974
Taxable Income:
To calculate the taxable income, we deduct certain deductions from the assessable income.
Deductions:
EPF contribution per month (deducted from salary) = Rs 5,878
Life insurance per month = Rs 3,300
Total deductions per year = EPF contribution + Life insurance = Rs 5,878 + Rs 3,300 = Rs 9,178
Taxable income = Assessable income - Total deductions = Rs 7,75,974 - Rs 9,178 = Rs 7,66,796
Income Tax:
To determine the income tax paid, we need to apply the applicable tax rate to the taxable income. Since tax rates can vary based on the country and specific rules, I am unable to provide the exact income tax amount without additional information.
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Chad created a table that shows the ratio of his sports game cards.Next, Chad created the graph below showing possible ratios for Pitchers cards to Infield cards in his deck. Which of the following statements are true?
Answer:
The 3rd answer is correct.
Step-by-step explanation:
The question involves a mathematical understanding of graphs and data interpretation, specifically ratios. To answer a question like this, typically, you would need to analyze both the graph and table for consistent ratio values. Though the question specifics are unclear, the broader concept involves understanding how ratios can be graphically represented.
Explanation:Given that the question involves ratios and cards, it appears to fall under a mathematical scope, specifically the interpretation of graphs and data. However, the information provided doesn't give specific details about Chad's data, the ratios of his sports game cards, or the graph he created that shows the possible ratios for Pitchers cards to Infield cards.
Typically, to validate any findings, you would need to look at the graph and the table. Comparing the values of the ratios in the table to the characteristics of the graph would help substantiate any claims. For instance, if Chad's graph shows that there's a 1:2 ratio of pitcher cards to Infield cards, this should be reflected in the table of his sports game cards.
Despite the ambiguous details in the question, you can still grasp the concept of ratios and how they can be represented graphically. For example, if you have a 3:5 ratio of oranges to apples, this can be depicted on a graph where one unit on the Y-axis represents 3 oranges and the corresponding unit on the X-axis signifies 5 apples.
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if 2540cm is increase by 15%, the result is
Answer:
2921
Step-by-step explanation:
[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]
125
(a) What is the measure of ange L?
(b) What is x?
(22-10)
I
(c) What is the measure of angle M?
65 N
The values of L and M in the triangle displayed are 55 and 60 respectively.
The value of angle L can be obtained thus :
125 + L = 180 (sum of angles in a triangle)
L = 180 - 125 = 55°
B.
The value of L can be calculated thus:
55 + (2x - 10) + 65 = 180 (sum of internal angles of a triangle)
120 + 2x - 10 = 180
110+2x = 180
2x = 180-110
x = 35
M = 2(35) -10 = 60°
Therefore, L = 55 and M = 60.
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What type of function is represented by the table of values below?
O A. exponential
B. linear
OC. cubic
D. quadratic
X
1
2
3
4
5
y
4
8
12
16
20
Answer:
B. linear
Step-by-step explanation:
You want to know the type of function represented by the table of values ...
x: 1, 2, 3, 4, 5y: 4, 8, 12, 16, 20DifferencesWhen the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.
Here, the "first differences" are ...
8 -4 = 412 -8 = 416 -12 = 420 -16 = 4They are constant with a value of 4.
The fact that first differences are constant means the function is a first-degree (linear) function.
The table represents a linear function.
__
Additional comment
The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.
The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.
If differences are not constant, but have a constant ratio, the function is exponential.
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MATH QUESTION HELP PLS!
Stephen predicted that he would sell 50 cakes at his school bake sale. However, only 45 were sold. What was Stephen's percent error?
pls helpppppppppppppppppp
Answer:
Step-by-step explanation:
Bisector means breaking the segment in half.
answer is A. to have a length exactly half the segment
What is the prime factorization of 625?
Answer:
5⁴
Step-by-step explanation:
625= 5×5×5×5
Write an inequality and solve.
Negative one hundred eighty three is at least nine more than 24 times a number.
Answer: -8 ≥ x
Step-by-step explanation:
Let x be the number, we set up an inequality:
-183 ≥ 9 + 24x [we use ≥ to present "at least"]
-192 ≥ 24x
-8 ≥ x
what is the quotient of the rational expressions shown below? make sure your answer is in reduced form x^2-16/x+5 divided by x^2-8x+16/2x+10
The quotient of the given rational expressions, (x^2 - 16)/(x + 5) divided by (x^2 - 8x + 16)/(2x + 10), is (x - 4)/(x - 4), which simplifies to 2.
To divide rational expressions, we invert the second expression and multiply it with the first expression. So, we have:
[(x^2 - 16)/(x + 5)] / [(x^2 - 8x + 16)/(2x + 10)]
To simplify this expression, we can multiply by the reciprocal of the second rational expression:
[(x^2 - 16)/(x + 5)] * [(2x + 10)/(x^2 - 8x + 16)]
Next, let's factorize the numerators and denominators of both expressions:
[(x + 4)(x - 4)/(x + 5)] * [2(x + 5)/((x - 4)(x - 4))]
Now, we can cancel out the common factors:
[(x + 4) * 2(x + 5)] / [(x + 5) * (x - 4)(x - 4)]
The (x + 5) factors cancel out:
[(x + 4) * 2(x + 5)] / [(x - 4)(x - 4)]
Further simplification:
[2(x + 4)(x + 5)] / [(x - 4)(x - 4)]
Now, we observe that the factors (x - 4)(x - 4) are the same in the numerator and denominator. Therefore, they cancel out:
2(x + 4)(x + 5) / (x - 4)(x - 4) = 2(x + 4)(x + 5) / (x - 4)(x - 4) = 2
Therefore, the quotient of the given rational expressions is 2.
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Given that g(x)=2x^2 - 2x + 9 , find each of the following.
a) g(0)
b) g(- 1)
c) g(2)
d) g( - x)
e) g(1 - t)
Answer:
Step-by-step explanation:
To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:
a) g(0)
To find g(0), substitute x = 0 into the function:
g(0) = 2(0)^2 - 2(0) + 9
g(0) = 0 - 0 + 9
g(0) = 9
b) g(-1)
To find g(-1), substitute x = -1 into the function:
g(-1) = 2(-1)^2 - 2(-1) + 9
g(-1) = 2(1) + 2 + 9
g(-1) = 2 + 2 + 9
g(-1) = 13
c) g(2)
To find g(2), substitute x = 2 into the function:
g(2) = 2(2)^2 - 2(2) + 9
g(2) = 2(4) - 4 + 9
g(2) = 8 - 4 + 9
g(2) = 13
d) g(-x)
To find g(-x), substitute x = -x into the function:
g(-x) = 2(-x)^2 - 2(-x) + 9
g(-x) = 2x^2 + 2x + 9
e) g(1 - t)
To find g(1 - t), substitute x = 1 - t into the function:
g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9
g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9
g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9
g(1 - t) = 2t^2 - 2t + 9
Therefore:
a) g(0) = 9
b) g(-1) = 13
c) g(2) = 13
d) g(-x) = 2x^2 + 2x + 9
e) g(1 - t) = 2t^2 - 2t + 9
Pregunta 1
Resuelve el siguiente problema aplicando las estrategias de solución de problemas.
• El área de un triángulo es de 30 pies cuadrados y la base mide 5 pies. ¿Cuál es la
altura del triángulo en pulgadas?
Answer:
I can't understand the language but try people who can
WHOEVER CAN ANSWER 50 POINTS IF U CAN SOLVE IT PLEASE IM DESPERATE
Answer:
First, the graph is overall decreasing with two local maximums and two local minimums.
Second, it has 5 zeros, since there is one intersection and two touching points with the x-axis.
Considering the above observations we can state that:
The degree of f(x) is odd;The leading coefficient is negative;There are 5 distinct zeros;There are 2 relative maximum values.A bank deposit paying simple interest grew from an initial amount of $1300 to $1365 in 3 months. Find the interest rate.
%/year
Answer:
the interest rate. : 5%
[(1365-1300)/1300]*100 = 5%
Step-by-step explanation:
find the value of x. 142 3x+22
Answer:
x = 40
you can guess and check.