How are the properties of exponents used when dividing a polynomial by a monomial?
Answer:
a couple different obes
Step-by-step explanation:
there are five
there is a certain number. If you add 30 7 to it, then subtract 22 7 from the previous result, and then subtract that difference from 59/7, after that you will get 19 7. What is a certain number?
Step-by-step explanation:
59 / 7 - ( x + 30 / 7 - 22 / 7 ) = 19 / 7
59 / 7 - ( x + 8 / 7 ) = 19 / 7
59 / 7 - x - 8 / 7 = 19 / 7
- x = 19 / 7 - 59 / 7 + 8 / 7
- x = - 32 / 7
x = 32 / 7
1. A bag contains 12 mangoes, of which 4 are not ripe.
What is the chance of picking at random a ripe mango from the bag ?
2. There are 12 red and 8 blue balls in a bag. If a ball is selected at random from the bag, what is the probability that it is
red ?
3. What is the number of all possible outcomes of tossing a fair die ?
4. A boy throws a fair die once. What is the probability of getting the number 4 ?
5. There are 10 red and 15 green balls in a bag.
Find the probability of selecting at random a red ball from the bag.
Answer:
1. 2/3 or 66.7%
2. 3/5 or 60%
3. 6
4. 1/6 or 16.7%
5. 2/5 or 40%
Step-by-step explanation:
In ΔABC, If AB=BC and ∠B=40∘,what is the measure of ∠C?
Answer:
70
Step-by-step explanation:
all angles in a triangle add up to 180
if two sides are equal their angles are equal
180-40
140÷2
70
A college student borrows $5000 to buy a car. The lender charges interest at an annual rate of 10%. Assume the interest is compounded continuously and that the student makes payments continuously at a constant monthly rate k. Determine the payment rate k that is required to pay off the loan in 5 years. What is the correct initial condition for this problem? A(O) = 0 A(O) = 5000 A(60) = -50000 A(5) = 0
The correct initial condition for this problem is A(O) = 5000.The differential equation governing the remaining balance R(t) after t years can be derived as follows:A'(t) = k - 0.1R(t),
where k is the constant monthly payment rate of the student.According to the given information, the interest is compounded continuously, which means we can apply the continuous compound interest formula to solve for R(t):R(t) = 5000 e^{0.1t}
The initial condition for this problem is that the student borrowed $5000,
so we have R(0) = 5000.We want to determine the payment rate k that is required to pay off the loan in 5 years, so we need to solve for k such that R(5) = 0:R(5) = 5000 e^{0.5} - k*12*5 = 0
Solving for k, we get:k = 5000 e^{0.5}/60 = 28.09
Therefore, the payment rate k that is required to pay off the loan in 5 years is $28.09 per month. The correct initial condition for this problem is A(O) = 5000.
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In the past, the output of a process had a mean of 2.050 and a standard deviation of 0.020 liters. If a current sample of output had these values {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, would that indicate that the process is still "in order" (as opposed to being "out of order")? What if the sample was {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}?
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."
To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.
For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:
Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):
Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.
Compare the sample mean to the known process mean (2.050):
The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."
Calculate the sample standard deviation using the formula:
Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))
Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.
Compare the sample standard deviation to the known process standard deviation (0.020):
The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."
For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:
Calculate the sample mean:
Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034
Compare the sample mean to the process mean (2.050):
The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."
Calculate the sample standard deviation:
The sample standard deviation is approximately 0.019 liters.
Compare the sample standard deviation to the process standard deviation (0.020):
The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.
In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.
However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.
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Two 50 foot tall radio towers are 3000 feet apart. Find the angle of depression from the top of one tower to the base of the other.
Answer:
Explanation:
The diagram representing the two towers is given below:
The distribution of mass for United States pennies minted since 1982 is approximately normal with mean 2.5 grams. A random sample of 10 pennies minted since 1982 was selected. The sample had a mean mass of 2.47 grams and a standard deviation of 0.04 gram. The test statistic for the population mean has which of the following distributions? (A) A normal distribution with mean 0 and standard deviation 1 (B) A normal distribution with mean 2.5 and standard deviation 0.04 (C) A normal distribution with mean 2.47 and standard deviation 0.04 (D) At-distribution with 9 degrees of freedom E At-distribution with 10 degrees of freedom
The test statistic for the population mean has a t-distribution with 9 degrees of freedom. Correct option is D.
The test statistic for the population mean in this scenario is a t-distribution with 9 degrees of freedom (option D).
To determine the test statistic, we need to use the formula:
t = (x' - μ) / (s / √n)
where x' is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
In this case, the hypothesized population mean is 2.5 grams, the sample mean is 2.47 grams, the sample standard deviation is 0.04 gram, and the sample size is 10.
Plugging these values into the formula, we get:
t = (2.47 - 2.5) / (0.04 / √10) ≈ -1.58
Since the sample size is less than 30, we use a t-distribution instead of a standard normal distribution. The degrees of freedom for the t-distribution is equal to n - 1, which in this case is 10 - 1 = 9.
We can use this distribution to calculate the p-value and make inferences about the population mean based on the sample data. Therefore, the correct option is D.
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A least-squares regression line is fit to a set of points. The total sum of squares is ∑(y i
− y
ˉ
) 2
=181.2, and the error sum of squares is ∑(y i
− y
^
i
) 2
=33.9. 18. Compute the coefficient of determination, r 2
.
The coefficient of determination, denoted as r^2, measures the proportion of the total variation in the dependent variable (y) that is explained by the independent variable(s) in a linear regression model. To compute r^2, we need the values for the total sum of squares (SST) and the error sum of squares (SSE). In this case, SST is given as 181.2 and SSE as 33.9.
The formula to calculate the coefficient of determination,\(r^2\), is given by r^2 = 1 - (SSE / SST). By substituting the provided values into the formula, we can compute r^2.
\(r^2 = 1 - (33.9 / 181.2)\)
\(r^2 = 1 - 0.1868\)
\(r^2 ≈ 0.8132\)
Therefore, the coefficient of determination,\(r^2\), is approximately 0.8132. This indicates that approximately 81.32% of the total variation in the dependent variable is explained by the independent variable(s) in the least-squares regression line. The remaining 18.68% represents the unexplained variation or the variability attributed to random error. A higher value of\(r^2\) suggests a stronger relationship between the variables, while a lower value indicates a weaker relationship.
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Find the value of x.
X
127X
Answer:
127
Step-by-step explanation:
x=127
corresponding angles
graph the linear function identify the x-intercept.
y=-x
The x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
What is the x-intercept?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = MX + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.So, plot the linear function:
Plot y = -x as follows:(Refer to the graph attached below)
We can clearly see that the x-intercept is 0.Therefore, the x-intercept of the given linear function is 0 and the graph of the linear ufnction is shown.
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I need help with solving for x. Then find the measure of the base angle. Please
Answer:
x = 8 base angle = 81 degrees
Step-by-step explanation:
Answer:
x = 8
base angle = 81 deg
Step-by-step explanation:
we observe that because the given triangle is a isosceles triangle, the base angles must be the same.
Hence the missing base angle must also be (10x+1)°
recall that all internal angles of an triangle must add up to 180 deg,
hence
180° = sum of all internal angles
180° = 18° + (10x+1)° + (10x+1)°
180° = 18° + 2(10x+1)° (subtracting 18 from both sides)
180 - 18 = 2(10x+1)
162 = 2(10x+1) dividing both sides by 2)
162 / 2 = 10x + 1
81 = 10x + 1 (subtracting 1 from both sides)
81 - 1 = 10x
10x = 80 (divide both sides by 10)
x = 80/10
x = 8 (answer)
substituting x = 8 into the expression for the base angle
base angle = (10x+1)
= 10(8) + 1
= 10 + 1
= 81
D(-1,4) and E (3,-2),
Answer:
(1,1)
Step-by-step explanation:
With the midpoint formula, we're basically finding the average of the two variables, x and y.
Formula: \((\frac{x_{1} + {x_2} }{2}, \frac{_{1} + {y_2} }{2} )\)
\((\frac{{-1} + {3}}{2} , \frac{{-2} + {4}}{2} )\)
\((\frac{2}{2}, \frac{2}{2})\)
(1,1)
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30 = 465
what function computes the value in which one-half of the data is above and one-half is below.
a. Middle
b. Mode c. average
d. Median
The RBIs for 15 players from the 2010 Seattle Mariners are shown.
15 51 35 25 58 33 64 43 33 29 14 13 11 4 10
Find the Median
Find the lower quartile
Find the upper quartile
Find the IQR
Find the Range
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on the z table with a 90% confidence interval, what is 1.645 called? group of answer choices critical value confidence interval margin of error point estimate
On the z-table with a 90% confidence interval, the value 1.645 is called the critical value. The critical value is used to determine the boundary values for the confidence interval. Correct option is A.
In a confidence interval, we use sample data to estimate the true population parameter with a certain degree of certainty or confidence. The critical value is determined based on the desired confidence level and the degrees of freedom (sample size - 1) of the distribution.
For example, if we want a 90% confidence interval, we use the z-table to find the critical value that corresponds to a probability of 0.05 in the tail of the distribution. The critical value represents the number of standard errors that correspond to the probability in the tail of the distribution.
Once we have determined the critical value, we can use it to find the margin of error for the confidence interval, which represents the range of values within which the true population parameter is likely to lie. The margin of error is calculated by multiplying the critical value by the standard error of the sample statistic.
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Complete question is:
On the z table with a 90% confidence interval, what is 1.645 called? group of answer choices
a. critical value
b. confidence interval
c. margin of error point
d. estimate
Help? 11 3/4 is the quotient of a number y and 6 1/4
Answer:
y divided by 6 1/4 = 11 3/4
Step-by-step explanation:
First, change the mixed numbers into improper fractions:
y divided by 25/4 = 47/4
Next, multiply both sides by 25/4:
y divided by 25/4 x 25/4 = 47/4 x 25/4
The 25/4's on the left side of the equation cancel each other out, leaving you with:
y = 47/4 x 25/4
Multiply 47 x 25 and keep the same denominator:
y = 1,175/4
Divide and:
y = 293 3/4
2.5z=10 write and solve equations
Answer:
z = 4
Step-by-step explanation:
2.5x = 10
divide by 2.5
z = 4
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what is the equation of a line perpendicular to 5y= -3x-10 passing through the point (3,-6)
In this case the answer is very simple .
Step 01:
Data
equation of the given line: 5y = -3x -10
y = -3/5x - 2
m = -3/5
given point: (3,-6) x1 = 3 y1 = -6
Step 02:
Slope of the perpendicular line, m’
m' = (-1) / m
\(m\text{'}=\frac{-1}{-\frac{3}{5}}=\frac{5}{3}\)Point-slope form of the line
(y - y1) = m (x - X1)
\((y\text{ - (-6)) = }\frac{5}{3}\cdot(x-3)\text{ }\)\(\begin{gathered} y\text{ +6=}\frac{5}{3}x\text{ -}\frac{5}{3} \\ y\text{ = }\frac{5}{3}x\text{ -}\frac{5}{3}-6 \\ \end{gathered}\)\(y\text{ = }\frac{5}{3}x\text{ -}\frac{23}{3}\)The answer is:
The equation of the perpendicular line is:
y = (5/3) x - (23/3)
according to the strict necessity test question 2 options: a. conclusions of inductive arguments do not follow by strict logical necessity from their premises b. conclusions of inductive arguments can follow by necessity from their premises if the argument's c. conclusion follows by strict logical necessity from its premises, it should be treated as deductive all of the above
According to the strict necessity test, Conclusions of inductive arguments do not follow by strict logical necessity from their premises. The correct option is a).
It means that even if the premises of an inductive argument are true, the conclusion can still be false, and the truth of the premises does not guarantee the truth of the conclusion.
Inductive reasoning involves making generalizations based on specific observations or evidence, but it does not provide conclusive proof like deductive reasoning. Therefore, the conclusions of inductive arguments are not necessarily true, even if the premises are true. So, The correct answer is a).
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Ethan buys 4 pack of muffins. he uses a coupon an saves 2$ off total.
Which expression represents his total cost?
Answer:
4x-2
Step-by-step explanation:
X=muffins
Find the measure of angle h
Answer:
62 degrees
Step-by-step explanation:
Since we know 3 sides of the triangle, we can use law of cosines.
\( {gk}^{2} = {gh}^{2} + {kh}^{2} - 2(gh)(kh) \times \cos(h) \)
\( {8}^{2} = {17}^{2} + {15}^{2} - 2(17(15) \times \cos(h) \)
\(64 = 289 + 225 - 510 \times \cos(h) \)
\(64 = 314 - 510 \times \cos(h) \)
\( - 250 = - 510 \times \cos(h) \)
\( \frac{250}{510} = \cos(h) \)
\( \frac{25}{53} = \cos(h) \)
Take the arcos or cosine inverse
\( \cos {}^{ - 1} = \frac{25}{53} \)
Which is about 62 degrees.
Question 1
Ben wants to fertilize the grass at a local park. The area of the grass-covered portion of the park is shaded in the diagram to the left. In square feet, what is the area of the grass-covered portion of the park?
A: 5,400
B: 6,880
C: 7,000
D: 8,600
Question 2
If a bag of fertilizer covers 500 square feet, how many bags of fertilizer will Ben need to purchase?
Answer:
Question 1: A - 5,400sqft
Question 2: 11 bags of fertilizer
Step-by-step explanation:
Question 1: You need the areas of the white squares added together and then subtracted from the total area of the park.
100 * 70 = 7,000 (The Park)20 * 60 = 1,200 (The Swings)20 * 20 = 400 (The Slide) 1,200 + 400 = 1,600 (The total white area)7,000 - 1,600 = 5,400 (The shaded area)Question 2: To find the number of bags needed to fertilize the grass we simply divide the area one bag can fertilize by the shaded area. We could use a basic equation such as:
500x = 5,400500x/500 = 5,400/500x = 10.8In this equation x represents the number of bags needed to fertilize the shaded area. The answer is 10.8, but logically speaking you cannot buy .8 of a bag so you just round up to 11.
Select the statements and reasons that complete the proof.
Statement #2. Reasons #1. And #3.
Answer:
Step-by-step explanation:
The first statement is the given statement, so the reason should be "given"
The reason on the second statement is reflexive, this means something is congruent to itself. So in the diagram, please see that angle C is in both triangles. It may be written as angle C or angle ACB or angle DCE is congruent to itself.
The reason the two triangles are similar is because they have two pairs of congruent angles (the first and second lines in the proof) This reason is AA which stands for angle-angle.
Answer:
1. a 2. c
Step-by-step explanation:
Determine the area of the trapezoid.
Answer:
A=87.5
Step-by-step explanation:
Hope im right and this helps you
the national survey of student engagement found that 24% of seniors report that they often or very often went to class without completing readings or assignments.12 assume that the sample size of seniors is 276,000. (a) find the margin of error for 99% confidence.
Margin of error for 99% confidence interval is 0.0021
What is confidence interval?
he range of values that, should you repeat your experiment or resample the population in the same manner, you would anticipate your estimate to fall within a particular percentage of the time.
Main Body:
Given :
99% Confidence Interval for p
p = 0.24,n = 276000
Significance level = α = 1− confidence = 1 − 0.99 = 0.01
Critical z-value = zα/2 = z0.01/2 = z0.005 = 2.58 (closest value From z table)
Standard e
or of p : SE =
√p× (1 − p)n=√0.24 × 0.76276000
≈ 0.0008129
E = zα/2 ×√p× (1 − p)n
= 2.58 × 0.0008129 ≈ 0.002097
Hence ,Margin of Error or, E = 0.00210
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© There is a bag with only milk and dark chocolates.
5
The probability of randomly choosing a dark chocolate is
5/12
There are 25 dark chocolates in the bag and each is equally likely to be chosen.
Work out how many milk chocolates there must be.
Answer:
I think it's 35, because if there's 25 dark and you divide 25 by 5 you get 5, so 1/12 is equal to 5
find the length of side x in simplest radical form with a rational denominator
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An isosceles trapezoid has perimeter of 70. Each of the congruent nonparallel sides has length 13, and the height of the trapezoid is 12. How long is the longest side?
The length of the longest side is 27 units, in the isosceles trapezoid.
What is isosceles trapezoid?
A four-sided shape called a trapezoid has two parallel lines on each side (normally the top and bottom sides). A trapezoid that has equal-length non-parallel sides (the legs) is said to be isosceles. Considering everything mentioned before, we may start learning how to calculate an isosceles trapezoid's perimeter.
Given, the congruent nonparallel sides has length 13.
he height of the trapezoid is 12.
the extra length of the larger side will be 2*x, as it will be extra portion in both side.
So x² = 13²-12²
x² = 169-144 = 25
x = √25 = 5
So the lentgh of the larger side is 10 unit larger than smaller side.
The perimer of the isosceles trapezoid will be P = sum of all sides
P = 2*13 + L + L+10
⇒70 = 26+10 +2L
⇒2L = 70 - 36
⇒2L = 34
⇒L = 17
The length of the larger side will be 17+10 = 27 units.
Hence the length of the longest side is 27 units.
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