The inverse of y = 7x² - 10 is √(x+10)÷7
What does mathematics inverse mean?Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effects of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One is the result when a number is multiplied by its reciprocal, or inverse.
based on the available facts;
y = 7x^2 - 10
Switch y and x.
x = 7y^2 - 10
Solve for y.
Add 10 to both sides.
x + 10 = 7y^2
Divide both sides by 7.
(x + 10)/7 = y^2
√ both sides.
√(x + 10)/7 = y
Replace y with f^-1(x)
f^-1(x) = √(x + 10)/7y = 7x^2 - 10
Switch y and x.
x = 7y^2 - 10
Solve for y.
Add 10 to both sides.
x + 10 = 7y^2
Divide both sides by 7.
(x + 10)/7 = y^2
√ both sides.
√(x + 10)/7 = y
Replace y with f^-1(x)
f^-1(x) = √(x + 10)/7
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Maria paid $240 for a table set after a discount of 40% . What was the original price? Use Scratchpad to show at least one model to solve the problem (e.g., tape diagram, table, double number line diagram, 10×10 grid).
The original price of the table set was $400.
What exactly is a discount?Customers are given discounts by shop owners in order to increase sales. A discount is a rebate or offer created to consumers on the listed price of goods.
A product's list price or marked price is the price proclaimed by the supplier or manufacturer, excluding any price reductions.The selling cost is the real price at which an article is sold after any reductions and discounts in the list price.Discounts are frequently described using words like "off" and "reduction."Now, as per the given question;
The paid price by Maria is $240 called selling price.
The total discount on the table set was 40%.
Let us consider the original price/marked price of the table set was 'x'.
Then the formula for calculating the original price/market price is;
Marked price - discount = selling price
x - 40%of x = 240
x - (40x)/100 = 240
100x - 40x = 24,000
60x = 24,000
x = 400
Therefore, the original price of the table set was $400.
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an invertible sheaf l on x is globally generated if and only if for any point p ∈ x, there is a global section of l not vanishing at p
an invertible sheaf l on x is globally generated if and only if for any point p ∈ x, there is a global section of l not vanishing at p
This fact leads to the first assumption naturally, but neither it nor the other implication can be proven.
What do you mean by vanishing?Vanishing means to leave or cease existing, especially in an abrupt or unexpected manner.
I be a quasicompact sheaf that can be inverted. X
demonstrate the existence of an epimorphism O ⊕I/X →I
OX⊕I→I if and only if for any point p∈X
p∈X there exists a global section of I
L not vanishing at p
If there is an epimorphism, it is asserted on page 121 of Hartshorne's book O ⊕I/X→I
OX⊕I→I Afterward, a family of global parts exists
{si} i∈I
{si}i∈I of I
I such that Ip is generated by {si,}i∈I
{si,p}i∈I as O
X,p
OX,p-module for every p∈X
This fact leads to the first assumption naturally, but neither it nor the other implication can be proven.
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Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and sd = 15. what conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
A conclusion which can be inferred about an individual score that corresponds to a z-value of 1.0 is that: c.) it is likely to come from the healthy distribution.
What is a z-value?A z-value is also referred to as a z-score or standard score and it can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.
In Statistics, z-values can either be positive or negative and it can be calculated by using this formula:
[tex]Z=\frac{x\;-\;u}{\delta}[/tex]
Where:
x is the sample mean or observed data.u is the mean.δ is the standard deviation.Since the individual score that corresponds to a z-value of 1.0, we can reasonably infer and logically conclude that an individual score is likely to come from the healthy distribution.
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Complete Question:
Scores of healthy adults on a neurological test form a normal distribution with mean = 100 and SD = 15. What conclusion can be inferred about an individual score that corresponds to a z value of 1.0?
a.) it falls in the general region of the population
distribution
b.) it falls in the common region of the distribution
c.) it is likely to come from the healthy distribution
d.) it is unlikely to come from the healthy distribution
i just need help asap please
Answer:
wsg
Step-by-step explanation:
Answer:
Step-by-step explanation:
need help on what
The drama club would like to build a theater in the round, so the audience can be seated on all sides of the stage, for its next production.
a. The stage is to be a regular octagon with a total perimeter of 60 feet. To what length should each board be cut to form the sides of the stage?
so if you take 60 by x and The sides of an octagon which is 8 you should have your answer
Can anybody help!!!??? Pls
Answer:
thanks for the points x
Step-by-step explanation:
thanks
Solve inequality.
-2 w<24
From the inequality given by -2w < 24, w is greater than -12.
Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.
Solving the inequality,
-2w < 24
Making sure the unknown variable is in one side and the constants in the other side.
-2w < 24
Divide both sides by -2, the coefficient beside the unknown variable,
(-2/-2)w < 24/-2
w < -12
Note that when we multiply or divide by a negative number
we must reverse the inequality.
w < -12 ⇒ w > -12
Therefore, w is greater than -12.
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Determine whether the data show a linear relationship. If so, write an equation of a line of fit.
The data do not show a linear relationship.
The data do not show a linear relationship.
The data show a linear relationship; The equation is y=4.25x+1.75.
The data show a linear relationship; The equation is y is equal to 4 point 2 5 x plus 1 point 7 5.
The data show a linear relationship; The equation is y=1.75x+4.25.
The data show a linear relationship; The equation is y is equal to 1 point 7 5 x plus 4 point 2 5.
The data show a linear relationship; The equation is y=6x.
The data show a linear relationship; The equation is y is equal to 6 x.
Question 2
If there is a linear relationship, use the selected equation to estimate y when x=15 and interpret its meaning in the context of the situation.
y=
, which means that after
minutes, you have burned
calories.
The slope of the given function is not constant therefore it will not be a linear function so option (A) will be correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
Given the data table,
If we take its point as coordinate then (1,6),(6,27),(11,50)(13,56) and (16,70).
Slope associated with two points (1,6), (6,27)
(27 - 6)/(6 - 1) = 4.2
Now Slope is associated with two points(6,27),(11,50)
(50 - 27)/(11 - 6) = 4.6
Since the slope is not the same therefore given function is not the linear function because the linear function has a constant slope.
Hence "The slope of the given function is not constant therefore it will not be a linear function".
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Eric teaches ceramics in his studio.he estimates that one out of every five people who call for information about a class will sign up for the class.last week he receive nine calls.find the probability that four or fewer of the people who called will sign up for a class
The probability that four or fewer of the people who called will sign up for a class = 0.9805
For given question,
Eric estimates that one out of every five people who call for information about a class will sign up for the class.
Last week he receive nine calls.
We need to find the probability that four or fewer of the people who called will sign up for a class.
Total number of calls = 9
⇒ n = 9
Since one out of every five people who call for information about a class will sign up for the class.
the probability of success (p) = 1/5
= 0.2
and the probability of failure (q) = 1 - p
= 1 - 0.2
= 0.8
To find the probability that four or fewer of the people who called will sign up for a class.
So, x would take values 0, 1, 2, 3, 4
Using Binomial principal,
For x = 0,
[tex]P(x=0)= ~^9C_0(0.2)^0(0.8)^{9-0}\\\\P(x=0)=0.13422[/tex]
For x = 1,
[tex]P(x=1)= ~^9C_1(0.2)^1(0.8)^{9-1}\\\\P(x=1)=0.30199[/tex]
For x = 2,
[tex]P(x=2)= ~^9C_2(0.2)^2(0.8)^{9-2}\\\\P(x=2)=0.30199[/tex]
For x = 3,
[tex]P(x=3)= ~^9C_3(0.2)^3(0.8)^{9-3}\\\\P(x=3)=0.17616[/tex]
For x = 4,
[tex]P(x=4)= ~^9C_4(0.2)^4(0.8)^{9-4}\\\\P(x=4)=0.06606[/tex]
So, the required probability would be,
P = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)
P = 0.1342 + 0.3020 + 0.3020 + 0.1762 + 0.0661
P = 0.9805
Therefore, the probability that four or fewer of the people who called will sign up for a class = 0.9805
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recall that the distance between a point and the xz-plane is the absolute value of its ? -coordinate.
Remember that a point's y-absolute coordinate's value determines how far away it is from the x-z plane.
With an example, define a plane?
Other names for it include a two-dimensional surface. A plane has an endless width, an infinite length, zero thickness, and also no curvature. The flat surfaces of a cube or cuboid, as well as the flat surfaces of paper, are all true examples of geometric planes, despite the fact that it is impossible to envision a plane in real life.A plane geometry is a closed, two-dimensional, or flat, figure. The properties of diverse plane shapes varies, such as the number of sides or corners (or vertices). A corner, also known as the vertex, is where two sides meet. A side is a straight line that forms a portion of the geometry.
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the following data was collected to explore how the average number of hours a student studies per night and the student's gpa affect their act score. the dependent variable is the act score, the first independent variable (x1) is the number of hours spent studying, and the second independent variable (x2) is the student's gpa. effects on act scores study hours gpa act score 6 2 30 4 4 25 3 4 25 2 2 19 1 4 27 step 1 of 2: find the p-value for the regression equation that fits the given data. round your answer to four decimal places.
The p-value is 0.1505 and y is 0.550x1 + 3.600x2 + 7.300.
What is a p-value?A p-value is a statistical measure used to test a hypothesis against actual data. A p-value estimates the likelihood of obtaining the observed results if the null hypothesis is true. The greater the statistical significance of the observed difference, the lower the p-value.So,
Given:
Study Hours GPA ACT Score
5 4 275 2 185 3 181 3 202 4 21Using technology, the P-value from the Fratio:
30.228571 / 8.190476 = 3.69 F = MSregression / MSresidualThe regression equation's P-value is:
Using the Fratio calculator's Value:
F(1, 3), 3.69 = 0.1505Using the P-value method:
At α = 0.01P-value >As a result, we cannot reject H0 and conclude that; there is insufficient evidence to demonstrate that the relationship is statistically significant.
The regression formula:
y = A1x1 + A2x2 +... AnXny = 0.550x1 + 3.600x2 + 7.300The predictor variables are x1 and x2.
y = variable predictedTherefore, the p-value is 0.1505 and y is 0.550x1 + 3.600x2 + 7.300.
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The complete question is given below:
The following data was collected to explore how the average number of hours a student studies per night and the student's GPA affect their ACT score. The dependent variable is the ACT score, the first independent variable (x1)is the number of hours spent studying, and the second independent variable (x2) is the student's GPA
Effects on ACT Scores
Study Hours GPA ACT Score
5 4 27
5 2 18
5 3 18
1 3 20
2 4 21
Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.
Step 2 of 2: Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.01 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.
Kathy has to write a 40 page report for her research class. She plans to write 8 pages in 4/7 week. She has 3 weeks to finish her report. Will she finish her report on time?
Answer:
Yes
Step-by-step explanation:
If she writes 8 pages a day for 4 days a week, in the first week, she will have already written 32 pages which she would only need one more day.
4 x 8 = 32
32 + 8 = 40
That gives her time to edit and revise :)
Hope this makes sense
What is the inverse funtion of F F(x)= 3-x/7
A. F-1(x)=3-7x
B. F-1(x)= 7+x/3
C. F-1(x)=3- x/7
D. F-1(x)= 7x - 3
Answer:
Replace y with f−1(x) f - 1 ( x ) to show the final answer. Verify if f−1(x)=x3+73 f - 1 ( x ) = x 3 + 7 3 is the inverse of f(x)=3x−7 f ( x ) = 3 x - 7
Step-by-step explanation:
if two groups of numbers have the same mean, then group of answer choices their standard deviations must also be equal. their medians must also be equal. their modes must also be equal. other measures of location need not be the same.
The correct answer is other measures of location need not be the same.
What is mean, mode, median and standard deviation?
When the group of numbers have the same mean then the other measures of location need not be the same. That means the standard deviation, median and mode should not be equal. All three widely used parameters that are mean, mode, median and standard deviation are the measure of central tendency.
If the given data has no outlier then mean value and the median value are closer to each other but the mode value is different. Similarly, standard deviation is calculated for the dispersion data. And it means when mean value is same then standard deviation will be different for a group of numbers.
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Solve for a
11 = -3/10a + 2
Answer:
a = -30
Step-by-step explanation:
In order to solve for a in the equation [tex]\sf 11 = \dfrac{-3}{10} a + 2[/tex], we can follow these steps:
Subtract 2 from both sides of the equation:
[tex]\sf 11 -2= \dfrac{-3}{10} a + 2-2[/tex]
[tex]\sf 9 = \dfrac{-3}{10} a[/tex]
Multiply both sides of the equation by [tex]\sf -\dfrac{10}{3}[/tex]:
[tex]\sf 9 *-\dfrac{10}{3}= \dfrac{-3}{10} a*-\dfrac{10}{3}[/tex]
-30 = a
Therefore, the solution to the equation 11 a + 2[tex]\sf \dfrac{-3}{10} a + 2[/tex] is a = -30.
if a circle passe though point (-4,2) and is tangent to the x-axis at (2,0), determine the coordinates of its center.
I need mathematical help asap
X-2x+3=3-x
Answer:
0 = 0
Step-by-step explanation:
Combine like terms: combine x and -2.
rearrange the terms on left side.
subtract 3 from both sides.
simplify (subtract -x and x)
0=0
4(u 1) - 1 = 2(2u - 3)
Answer:
4u+4-1=4u-6
4u+3=4u-6
4u+9=4u
9 I think
Step-by-step explanation:
Tom does not really want to give away blue marbles and would like to change the probability that he chooses a blue marble to 1/10. How many marbles that are not blue could he add to the bag so that the probability of choosing a blue marble becomes 1/10?
Answer:
9
Step-by-step explanation:
if one marble is blue and 9 are other colors than its a 1/10 chance of getting a blue marble
What's 59.84 ÷ 32 please show work I have test tomorrow
If y varies inversely as x cubed, and y = 12 when x = 5, find the value of y when x = 2.
Answer:
187.5
Step-by-step explanation:
[tex]\sf {If \; y \; varies \; inversely \; as \; x^3\; represented \; by\; y\propto \dfrac{1}{x^3}} \\then\\y = \dfrac{k}{x^3}\; where\; k \;is\; a \;constant\\\\== > k = y\cdot x^3\\\\When y = 12, x = 5 \;means\\\\k = 12.\cdot 5^3 = 12 \cdot 125 = 1500\\\\\sfTherefore \;when\; x = 2\\y = \dfrac{1500}{2^3} = \dfrac{1500}{8} = 187.5\\\\\sf Answer:\;\; \boxed {\sf y = 187.5\; \sf when\; x = 2}[/tex]
-(10 + (-6))
-((-55) + 1
-2
Answer:
52
Step-by-step explanation:
-(10 + (-6)) - ((-55) + 1 - 2)
(-10 + 6) + (55 - 1 + 2)
(-4) + (56) = 52
I hope this helps!
Boris and Chip are playing a game with number cubes. They roll two cubes and subtract the two numbers. If the difference is 5, Boris wins. If the difference is 4, Chip wins. Is the game fair? Explain.
The computation shows that the game is not fair
How to illustrate the information?It should be noted that the cube had numbers 1 to 6. Therefore, the difference of 4 can be either 6-2 or 5-1 .
On the other hand, the difference of 5 will only be 6-1.
Therefore, this is not fair
In conclusion, the game is not fair.
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Find the x-intercept of the graph of y = x -2.
x-intercept:(,0)
Find the quotient for -12 ÷ (-3).
a. -9
b. 4
c. -4
Answer:
b. 4
Step-by-step explanation:
A negative number divided by a negative number is a positive number.
Therefore, -12 ÷ -3 = 4.
Please help i will give out brainlist
1) The converse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you do not like sea food, then you will go to an Italian restaurant"
2) The inverse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you go to an Italian restaurant, then you don't like sea food"
3) The contrapositive of "If you do no go to an Italian restaurant, then you like sea food" is; If you do not like sea food, then you will go to an Italian Restaurant"
How to Interpret Conditional Statements?1) The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." Thus, the converse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you do not like sea food, then you will go to an Italian restaurant"
2) The inverse of a conditional statement is when both the hypothesis and conclusion are negated. Thus, the inverse of "If you do no go to an Italian restaurant, then you like sea food" is; "If you go to an Italian restaurant, then you don't like sea food"
3) The contrapositive of a conditional statement is to interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain.". Thus, the contrapositive of "If you do no go to an Italian restaurant, then you like sea food" is; If you do not like sea food, then you will go to an Italian Restaurant"
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Find the area of the rhombus
9 in
12 in
A = [?] in?
Answer:
A=54in squared.
Step-by-step explanation:
To answer this you need to know two numbers which in this case is 9 and 12. 12 will be called the Base for now and 9 the height. and they you multiply them together to get 108 but it is like a triangle next you need to half the number so half of 108 is 54.
there are also many different calculators that all you need to do is input the numbers and it will tell you I hope this is helpful to you and that you will get the right answer.
What is the domain?
-3,5
0,4
3,5
Answer:
-3, 0, 3
Step-by-step explanation:
The domain is the set of all x values
What is the shape of the distribution for the following set of data? x f 5 5 4 3 3 1 2 3 1 5
The shape of the distribution for the following set of data is: symmetrical.
What are distributions?When we study data, one of the major ways to understand it is to think about its general form, such as whether it is symmetrical, has more numbers on one side than the other, or fits a common probability distribution like the normal, binomial, or exponential.
Now,
By looking at how the data are arranged in the table, we can tell that the distribution's form is symmetrical. With 1 item at X=3, it appears that this occurs frequently. The average was calculated using the range of data from X=1 to X=5. In addition, the data contain 5 items at X=5 and X=1, respectively. Both of these occur equally often and at equal intervals from the average. We can also say that there are three items in the data at X=4, three things at X=2, and so on, all of which are equally far from the average. As a result, every piece of data is either averaged out or counterbalanced on the other side of the average. A symmetrical distribution is described here. Therefore, it is neither favorably nor negatively biased. Even though it is symmetrical, the distribution is not normal since a normal distribution contains more data at the average than at the tails, as opposed to fewer.Hence, The shape of the distribution for the following set of data is: symmetrical.
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What is the scale factor of the dilation of figure A to figure B?
a. 2/3
b. 3/2
c. 2
d. 3