Using algebra, the numbers multiply by 10 and add up to -10 are -5 - √(15) and -5 + √(15).
To find two numbers that multiply to 10 and add up to -10, we can use algebra. Let's call the two numbers we're looking for x and y. We know that:
xy = 10
We also know that:
x + y = -10
Now we can solve for one of the variables in terms of the other. For example, we can solve for x in terms of y by rearranging the second equation:
x = -y - 10
Now we can substitute this expression for x into the first equation:
(-y - 10)y = 10
Expanding and simplifying, we get:
-y² - 10y - 10 = 0
Solving for y using the quadratic formula, we get:
y = (-(-10) ± √((-10)² - 4(-1)(-10))) / (2(-1))
y = (10 ± √(60)) / 2
So the two possible values for y are:
y = 5 + √(15)
y = 5 - √(15)
Finally, we can plug each of these values for y back into x = -y - 10 to get the corresponding values for x:
x = -5 - √(15)
x = -5 + √(15)
Therefore, the two numbers that multiply by 10 and add up to -10 are approximately -5 - √(15) and -5 + √(15).
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why are 4:7, 8:15, 16:28, 20:35 equivalent
Answer:
I am assuming the 8:15 was a typo and was actually supposed to be a 8:14. Anyways, they are equivalent because they all make 4:7 when simplified.
Step-by-step explanation:
4:7 = itself at this point, as they don't have numbers that can simplify each other on both sides, unless you are looking for a decimal answer.
8:14 = 4:7 <- You can divide the 8 and 14 by two. 8 divided by 2 is four, and 14 divided by 2 is 7.
16:28 = 4:7 <- You can divide the 16 and the 28 by four. 16 divided by 4 is 4, and 28 divided by 4 is 7.
20:35 = 4:7 <- You can divide both sides by 5. 20 divided by 5 is 4, and 35 divided by 5 is 7.
What is the solution to 6x2 –14x ≥ –4?
Answer:
2.85714285714
Step-by-step explanation:
6x2 –14x ≥ –4
36 -14x ≥ -4
-14x ≥ -36-4
-14x ≥ -40
x ≥ -40/14
x \(\leq\) 2.85714285714
A
Step-by-step explanation:
did math
I need the answers please !
Answer:
m<5 = 133°
m<8 = 47°
Step-by-step explanation:
if <2 = 47°, and <5 is supplementary to <2, that means that together they both have to equal 180°. So, to get the measure of <5, you need to do 180 - 47 to get <5 = 133°.
Now, <5 (133°) is supplementary to <8, so they both have to equal 180° together. So, you must do 180 - 133 to get <8 = 47°. Or, another way to get <8 is to notice that <2 and <8 are alternate interior angles, which means they equal the same amount. So if <2 = 47°, then so does <8.
State three "real-world" variables X, Y, and Z for which you expect a marginal association between X and Y but conditional independence controlling for Z.
Three "real-world" variables for which you expect a marginal association between X and Y but conditional independence controlling for Z are:
- X = Hours spent studying
- Y = Grades in school
- Z = Intelligence
In this scenario, there is a marginal association between the hours spent studying (X) and the grades in school (Y), as it is expected that the more time a student spends studying, the better their grades will be.
However, when controlling for intelligence (Z), the association between X and Y becomes conditional independence, as intelligence can also affect grades in school.
In other words, the relationship between X and Y is no longer significant when controlling for Z.
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PLS HELP ME WITH THIS ASAP PLS
Answer:
A) x(x-1)(x+1)
Step-by-step explanation:
In the second term on the LHS, the denominator \(x^2-1=(x-1)(x+1)\), and \(x-1\) is contained in the first term. Therefore, the least common denominator would be \(x(x-1)(x+1)\).
A container full of fruit punch weighs 275 oz. The empty container weighs 45 oz. How much does a half-filled container weigh?
Answer:
A half-filled container will weight 160 oz
Step-by-step explanation:
Weight of container with fruit punch = 275 oz
weight of container excluding fruit punch = 45 oz
Weight of fruit punch = Weight of container with fruit punch - weight of container excluding fruit punch = 275 oz - 45 oz = 230 oz
Thus, when container is full, it contains 230 oz.
When container will be half full, it will contain half of 230 oz
half of 230 oz = 1/2 * 230 oz = 115 oz
Thus,
a half-filled container will weight = weight of container + half of the capacity of container(115 oz) = (45 + 115) oz = 160 oz.
Thus, a half-filled container will weight 160 oz.
10. The average resting heart rate of a population is 87 beats per minute, with a standard deviation of 11 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.(a) 110 bpmz = (b) 80 bpmz =
The formula for determining the z score is expressed as
z = (data value - mean)/standard deviation
a) data value = 110
mean = 87
standard deviation = 11
z = (110 - 87)/11
z = 2.09
b) data value = 110
mean = 80
standard deviation = 11
z = (80 - 87)/11
z = - 0.64
18. If f(x) = arccos(x^2), then f'(x) =
The derivative of f(x) = arccos(x^2) is: f'(x) = -2x / √(1-x^4)
The derivative of f(x) = arccos(x^2), we'll use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is arccos(u) and the inner function is u = x^2.
First, let's find the derivative of the outer function, arccos(u). The derivative of arccos(u) is -1/√(1-u^2). Next, we'll find the derivative of the inner function, x^2. The derivative of x^2 is 2x.
Now we'll apply the chain rule. We have:
f'(x) = (derivative of outer function) * (derivative of inner function)
f'(x) = (-1/√(1-u^2)) * (2x)
Since u = x^2, we'll substitute that back into our equation:
f'(x) = (-1/√(1-x^4)) * (2x)
So, the derivative of f(x) = arccos(x^2) is:
f'(x) = -2x / √(1-x^4)
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Write the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
Gwen participates in an online rewards program. she earned points for completing surveys. Gwen earns 10 points for each survey she completes and she wants to predict the total number of points she will earn based on the number of surveys she completes.
The total number of points earned for completing x surveys is 10x.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Points earned for each survey = 10
Now,
The total number of points earned for x survey.
= 10x
Thus,
The total number of points earned for completing x surveys is 10x.
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Which of the following exponential functions represents the graph below?
O A Rx) = 1 • 3*
O B. f(x) = 10
O c.
C. 12-23
OD. f(x) = 3.1
The exponential function represented on the graph is f(x) = (1/3)\(.^x\). The correct option is B.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The given graph is representing the exponential function f(x) = (1/3)\(.^x\) The graph is attached with the answer below. The graph is showing the inverse fraction of ( 1/3).
Therefore, the exponential function represented on the graph is f(x) = (1/3)\(.^x\). The correct option is B.
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Expand and simplify
(x + 1)(x + 2)(x + 3)
A stoplight is green for 28 seconds, yellow for 5 seconds, red for 27,seconds. what is probability that the light will not be green when you arrive
Therefore, the probability that the light will not be green when you arrive is approximately 0.5333 or 53.33%.
Total time for one complete cycle = green time + yellow time + red time
= 28 seconds + 5 seconds + 27 seconds
= 60 seconds
The probability that the light will not be green when you arrive can be calculated by dividing the time for which the light is not green (yellow + red) by the total time for one complete cycle.
Probability = (yellow time + red time) / total time for one complete cycle
= (5 seconds + 27 seconds) / 60 seconds
= 32 seconds / 60 seconds
≈ 0.5333 (rounded to four decimal places)
Therefore, the probability that the light will not be green when you arrive is approximately 0.5333 or 53.33%.
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The purchased cost of a 5-m3 stainless steel tank in 1995 was $10,900. The 2-m-diameter tank is cylindrical with a flat top and bottom. If the entire outer surface of the tank is to be covered with 0.05-m-thickness of magnesia block, estimate the current total cost for the installed and insulated tank. The 1995 cost for the 0.05-m-thick magnesia block was $40 per square meter while the labor for installing the insulation was $95 per square meter.
The estimated current total cost for the installed and insulated tank is $12,065.73.
The first step is to calculate the surface area of the tank. The surface area of a cylinder is calculated as follows:
surface_area = 2 * pi * r * h + 2 * pi * r^2
where:
r is the radius of the cylinder
h is the height of the cylinder
In this case, the radius of the cylinder is 1 meter (half of the diameter) and the height of the cylinder is 1 meter. So the surface area of the tank is:
surface_area = 2 * pi * 1 * 1 + 2 * pi * 1^2 = 6.283185307179586
The insulation will add a thickness of 0.05 meters to the surface area of the tank, so the total surface area of the insulated tank is:
surface_area = 6.283185307179586 + 2 * pi * 1 * 0.05 = 6.806032934459293
The cost of the insulation is $40 per square meter and the cost of labor is $95 per square meter, so the total cost of the insulation and labor is:
cost = 6.806032934459293 * (40 + 95) = $1,165.73
The original cost of the tank was $10,900, so the total cost of the insulated tank is:
cost = 10900 + 1165.73 = $12,065.73
Therefore, the estimated current total cost for the installed and insulated tank is $12,065.73.
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To divide
by
, answer this question: How many sets of
are in
? Use the model representing the fraction
to help you answer the question. (Hint: Think about grouping the blue boxes into pairs.)
Solve for x. 2(-5x+4)+4x-5=-3
Let's factor out first. 2(-5x+4)+4x-5 = -10x+8+4x-5. If we combine like terms, -10x+8+4x-5 is -6x+3. Now our equation looks like this:
-6x+3 = -3.
If we move over the 3 on the left to the right side, we have -6x = -6. Divide both sides by -6, and we get our answer.
x = 1
Hope this helped!
In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla
Answer: 3
Step-by-step explanation: just do 15+13+10 which is 38 And then subtract 35 from 38 which gives you your answer 3
Can someone explain the answer to 7.1x10^-3 ?
Answer:
\({ \tt{7.1 \times {10}^{ - 3} }} \\ { \bf{negative \: means \: { \green{increase \: in \: decimal \: places}}}} \\ = { \tt{0.71 \times {10}^{ - 2} }} \\ = { \tt{0.071 \times {10}^{ - 1} }} \\ = { \tt{0.0071 \times {10}^{0} }} \\ { \boxed{ but \: {10}^{0} = 1}} \\ \therefore{ \tt{ = 0.0071 \times 1 = 0.0071}}\)
Pls help I’ve been stuck on this for a while
Answer:
Step-by-step explanation:
Abd and dbc are linear pairs, and abd and evc are vertical angles. if mabd = 5(2x + 1), mdbc= 3x + 6, and mebc = y+135/2, select all statements that are true
The following statements are true:
mabd + mdbc = 180 degrees
mabd = mevc
What are the true statements given that abd and dbc are linear pairs, abd and evc are vertical angles, and the measures are given?According to the definition of linear pairs, the two angles add up to 180 degrees. Therefore, mabd + mdbc = 180 degrees.
According to the definition of vertical angles, they have the same measure. Therefore, mabd = mevc.
Since abd and evc are vertical angles, and mabd = mevc, then mabd = mebc. Therefore, we can substitute mabd in the equation mebc = y+135/2 to get 5(2x + 1) = y+135/2.
We can solve for y to get y = 10x + 260.
Now we can substitute this value of y into the equation mebc = y+135/2 to get mebc = 10x + 347.5.
Therefore, none of the statements in the question that mention mebc are necessarily true or false, since we don't have enough information about the value of x to determine its measure.
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11. Which regular polygon has a minimum rotation of 45° to carry the polygon onto itself?
A. octagon
B. decagon
C. hexagon
D. pentagon
Answer:
the answer is a octagon that has rotation of 45degrees
tb mc qu. 5-78 (algo) thane company is interested in establishing the... thane company is interested in establishing the relationship between electricity costs and machine hours. data have been collected and a regression analysis prepared using excel. the monthly data and the regression output follow: month machine hours electricity costs january 2,100 $ 19,000 february 2,500 $ 22,200 march 1,500 $ 14,100 april 2,700 $ 24,200 may 3,400 $ 28,850 june 2,900 $ 23,200 july 3,700 $ 25,350 august 3,100 $ 23,350 september 1,600 $ 16,700 october 3,300 $ 27,200 november 4,300 $ 32,200 december 3,800 $ 28,350 summary output regression statistics multiple r 0.959 r square 0.919 adjusted r2 0.911 standard error 1,558.51 observations 12.00 coefficients standard error t stat p-value lower 95% upper 95% intercept 6,967.32 1,631.91 4.27 0.00 3,331.20 10,603.44 machine hours 5.76 0.54 10.68 0.00 4.56 6.96 based on the results of the regression analysis, the estimate of electricity costs in a month with 1,800 machine hours would be: (rounded to the nearest whole dollar)
Based on the results of the regression analysis, the estimate of electricity costs in a month with 1,800 machine hours would be $17,695.32
The regression coefficients are also important in determining the relationship between the variables. In this case, the intercept is 6,967.32 and the coefficient for machine hours is 5.76.
This means that the estimated cost of electricity per month is $6,967.32 when there are zero machine hours. For each additional machine hour, the estimated cost of electricity increases by $5.76.
To estimate the cost of electricity in a month with 1,800 machine hours, we can use the regression equation:
Electricity cost = intercept + (coefficient x machine hours)
Plugging in the values, we get:
Electricity cost = 6,967.32 + (5.76 x 1,800)
Electricity cost = $17,695.32 (rounded to the nearest whole dollar).
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Pls help this whole problem is so confusing. HELP
1. 5*20= 100
2.3.18309886184
3.6.36619772368
4.20
5.The choice of a circular table or a rectangular table depends on a variety of factors such as the intended use, available space, and personal preferences. However, there are some advantages to using a circular table over a rectangular one:
More inclusive: A circular table allows for more inclusive conversations since everyone can see and hear each other. There is no "head" of the table, which can make some people feel excluded.
Easier to navigate: A circular table allows for easier navigation around the table. There are no corners to bump into, and people can move around the table more freely.
Better for small spaces: A circular table can be more efficient for small spaces since it takes up less floor space than a rectangular table with the same seating capacity.
Aesthetically pleasing: A circular table can be aesthetically pleasing and can add a touch of elegance to a room. It can also create a more intimate and cozy atmosphere.
However, a rectangular table can also have advantages. It can be more practical for certain activities such as working on projects or serving food. It may also be easier to fit into a particular space or room layout. Ultimately, the choice of table shape depends on the specific needs and preferences of the user.
A pair of shoes usually sells for $59. If the shoes are 30% off, and sales tax is 6%, what is the total price of the shoes, including tax
Answer: 43.778
Step-by-step explanation: i am guessing thats the answer
3. Find the value of r so the line that passes through (7,r) & (1, -1), has a slope ofm=į (9 pts)Hi can Someone please help !
You have the following points:
(7,r)
(1,-1)
and you have to find the value of r, that makes that the line which crosses the previous points has a slope of m = 1/2.
To find the value of r, you use the following formula for the slope m:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are two point of the line.
The points are:
(x1,y1) => (1,-1)
(x2,y2) => (7,r)
replace the previous values in the formula for the slope m, and solve for r:
m = (r - (-1))/(7 - 1)
m = (r + 1)/(6) multiply both sides by 6
6m = r + 1 subtract both sides by 1
6m - 1 = r replace the value of m = 1/2
6(1/2) - 1 = r
3 - 1 = r
2 = r
Hence, the value of r has to be r = 2 for getting a slope of m = 1/2 of a line which crosses the given points
why the evidence in the form of the p-value should not be considered conclusive that ms. gilbert was guilty of the excess death? (think about cobb’s arguments)
Cobb's arguments about p-value is about the uncertainty of data that p-value represents. It doesn't signify truth and must be comprehended in the setting of other variables.
A p-value of 0.05 specifies that the possibility of observing the result by chance is 5%, but the other aspect of that is that it also shows that there is a 95% probability of obtaining a result that is not due to chance.
Cobb argues that other variables such as multiple testing, confounding variables, or sampling variability can affect the p-value's precision. The p-value is considered invalid in the presence of any
or sampling variability, as it may mislead the results. A p-value is also vulnerable to multiple testing, which is when numerous evaluations are done on the same data. When performing multiple testing, a more conservative p-value is required to regulate for the risk of an accidental Type I error.
Cobb's argument emphasizes that while the p-value is essential for hypothesis testing, it should not be the sole determinant of data's validity. Researchers must consider other sources of variability when interpreting p-values to determine if they support or refute a hypothesis.
Hence, p-value alone should not be considered conclusive, and one must consider other sources of data to make decisions.
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Which equation has an X intercept of 5 and a Y intercept of 10?
C) 2x+y=10 is the line has an X intercept of 5 and Y intercept of 10
To find the eqaution of line whose X intercept and Y intercept is given we will use line intercept form of line
The equation of line with A units of X intercept and B units of
Y intersect is given by:
\(\frac{x}{A} + \frac{y}{B} =1\) ----(i)
given that A= 5 (X intercept) and B= 10 (Y intercept)
so equation (i) reduces to
\(\frac{x}{5}+\frac{y}{10} =1\)
so 2x + y = 1*10
so the equation of the line is 2x+y=10
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Complete question:
Which equation has an X intercept of 5 and a Y intercept of 10?
A) 3x+2y=10
B) 5x+7y=2
C) 2x+y=10
D) 11x+7y=9
The estimate on an explanatory variable is not statistically significant at the 5%-level if the t-statistic is greater than 2.5. the p-value is less than 0.05. the 95% confidence interval does not contain zero. the 95% confidence interval contains zero.
The estimated value of the explanatory variable is not statistically significant at the 5%-level if a. the t-statistic is greater than 2.5.
The t-test is a hypothesis testing technique used to decide whether the estimated coefficient of a linear regression model is statistically significant or not. The t-value is used to measure the size of the difference between the estimated coefficient and the hypothesized value. When the t-value exceeds a critical value, such as 2.5, the estimated value of the explanatory variable is not significant at the 5%-level. It implies that the null hypothesis, which assumes that the explanatory variable's coefficient is zero, cannot be rejected.
The p-value is a measure of the probability of obtaining a more extreme value of the test statistic than the observed value if the null hypothesis is true. A small p-value implies that the null hypothesis should be rejected. When the p-value is less than 0.05, it means that the estimated value of the explanatory variable is significant at the 5%-level.
The confidence interval is a range of values that is expected to include the true value of the population parameter with a specified level of confidence. A 95% confidence interval means that the true value of the population parameter lies within the range 95% of the time. The 95% confidence interval does not contain zero implies that the estimated value of the explanatory variable is statistically significant at the 5%-level since it suggests that the population parameter is different from zero at the 5%-level. Conversely, if the 95% confidence interval contains zero, the estimated value of the explanatory variable is not statistically significant at the 5%-level since it means that the population parameter is not different from zero at the 5%-level. Therefore, it is essential to examine the t-statistic, p-value, and confidence interval while conducting hypothesis testing to make an informed decision.
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this is confusing i need help ;-;
Answer:
B I think
Step-by-step explanation:
What is the rule of SAS criteria?
We have defined the criteria for SAS congruency of triangles.
What is SAS?
The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."
According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.
Hence, we have defined the criteria for SAS congruency of triangles.
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