Answer:
First, we can calculate the discount from the sale. The sweater costs $65.99, and with a 40% discount, the price is reduced by:
$65.99 x 0.40 = $26.40
So the sale price of the sweater is:
$65.99 - $26.40 = $39.59
Next, we can apply Carson's $10 coupon to the sale price:
$39.59 - $10 = $29.59
Therefore, Carson pays $29.59 for the sweater after the discounts.
To calculate the total discount that Carson receives, we can first find the amount of the 40% discount on the sweater, which is:
40% of $65.99 = 0.4 x $65.99 = $26.40
Then, we can add the additional $10 coupon discount to get the total discount:
$26.40 + $10 = $36.40
Therefore, the total discount that Carson receives on the sweater is $36.40.
To find the final price that Carson pays after the discounts, we can subtract the total discount from the original price:
$65.99 - $36.40 = $29.59
Therefore, Carson pays $29.59 for the sweater after the discounts.
Liam estimates that the distance between City A and City B is 85 miles. The actual
distance between the two cities is 84.5 miles. What is the percent error in Liam's
estimate?
Answer:
0.5 difference
Step-by-step explanation:
since liam estimated 85 miles even though it is 84.5, you should minus 85 from 84.5 which will equal 0.5
The function f(x) = 1590.85)^x models the height, in feet, of a bouncing ball after x seconds.
What is the initial height of the bouncing ball?
What is the percent rate of change?
What is the height of the bouncing ball after 5 seconds? express your answers as a decimal rounded to the nearest hundredth.
In the function,
1) Initial height of the bouncing ball is 15feet.
2) The percent rate of change is -16.25%
3) The height of the bouncing ball after 5 seconds is 6.65 feet.
What is function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
There seems to be a typo in the function you provided. I will assume that the function is:
=> f(x) = [tex]15(0.85)^x[/tex]
Assuming this is correct, here are the answers to your questions:
The initial height of the bouncing ball is the value of the function when
x = 0, which is:
=> [tex]f(0)=15(0.85)^0=15ft[/tex]
Therefore, the initial height of the bouncing ball is 15 feet.
The percent rate of change of the function can be found by taking the derivative of the function and expressing it as a percentage.
The derivative of the function is:
=> f'(x)= [tex]\frac{15ln(17)\times17^x-15ln(20)\times17^x}{20^x}[/tex]
The percent rate of change is then:
=> [tex]\frac{f'(x)}{f(x)} \times100\%[/tex]
=> [tex]\frac{\frac{15ln(17)\times17^x-15ln(20)\times17^x}{20^x}}{15(0.85)^x}[/tex]
=> [tex]ln(\frac{17}{20})[/tex]
=> -16.25%
Therefore, the percent rate of change of the function is approximately:
=> -16.25%
The height of the bouncing ball after 5 seconds is: then x=5
=> [tex]f(5)=15(0.85)^5[/tex]
Rounding this to the nearest hundredth, we get:
=> 6.65 feet
Therefore, the height of the bouncing ball after 5 seconds is approximately 6.65 ft.
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need help on this asap
3. Put the following integers in the descending order: -1, 10, -12, 0, -100, 100, 105
the diagram shows a triangular face of the pyramid of cestius in rome italy. the length of the base of the triangle is 30 meters. the lengths of the other two sides of the triangle are both 36 meters.
Answer: i will be able to help if i see the question??
Step-by-step explanation:
Help please! No silly answers. Correct answers would be very much appreciated! Please try and do this as soon as possible (ASAP) Thank you all.
Answer:
y = -3x + 1
Step-by-step explanation:
y = mx + b
mx: slope
b: y-intercept
This line has a negative slope (mx) because of its direction. The plotted points are three units down and one unit right apart, which makes it -3/1x or -3x.
The y-intercept (b) is 1 because at the coordinate (0, 1) the line passes through the y-axis.
Therefore, the line should be y = -3x + 1.
Use the graph to answer the question. Graph of polygon ABCD with vertices at negative 6 comma negative 2, negative 4 comma 5, 1 comma 5, negative 1 comma negative 2. A second polygon A prime B prime C prime D prime with vertices at negative 6 comma 2, negative 4 comma negative 5, 1 comma negative 5, negative 1 comma 2. Determine the line of reflection used to create the image. x = 2 y = 2 y-axis x-axis
The line of reflection used to create the image is the y-axis. The x-axis is the line of reflection utilized to produce the picture of polygon ABCD to A' B' C' D'. The y-coordinates of each vertex.
in A' B' C' D' are the inverse of the corresponding y-coordinates in ABCD, but the x-coordinates stay constant. The x-axis is a horizontal line that goes through the origin and mirrors points that cross it. As a result, when each point in ABCD is mirrored across the x-axis, the point in A' B' C' D' is produced. As a result, the transformation that maps ABCD to A' B' C' D' is an x-axis reflection. the graph to answer the question. Graph of polygon ABCD with vertices at negative 6 comma negative 2, negative 4 comma 5, 1 comma 5, negative 1 comma negative 2.
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I need help with the Surface Area of Pyramids and Cones
Will give Brainliest
Answer:
Step-by-step explanation:
If you don't know, the Pythagorean Theorem states that a^2+b^2=c^2 in a right triangle where a and b are the legs and c is the hypotenuse.
Imagine unfolding a cone. It would become part of a circle. Therefore, to find the lateral surface area(the surface are not including bases), you have to find the surface area of this part of the circle. The circumference of the entire circle is 6*pi*sqrt10. The circumference of this partial circle is the circumference of the base of the cone which is 2*3*pi=6pi. therefore, the percent of the circle is 6*pi/6*pi*sqrt10=1/sqrt10. 1/sqrt10*90pi=90*sqrt10*pi/10=9*sqrt10*pi.
the area of the base is 3^2*pi=9pi. the answer is then 9pi(1+sqrt10)
commuting to work ~ jeremy works for a well-known marketing firm and needs to gather information about individuals in a test market for a new client. jeremy wants to calculate a 95% confidence interval for the proportion of adults in the test market who commute more than 20 miles one-way to work each day. jeremy is unable to find any preliminary information about what the proportion may be, but he wants to have a margin of error of no more than 0.04. how large a sample size will jeremy need?
Jeremy needs a sample size of at least 601 to estimate the proportion of adults in the test market who commute more than 20 miles one-way to work each day with a 95% confidence interval and a margin of error of 0.04.
To calculate the sample size required, we need to use the formula:
n = (z^2 * p * (1-p)) / E^2
where:
n = sample size
z = z-score associated with the desired confidence level (95%)
p = estimated proportion (0.5, since we have no preliminary information)
E = maximum margin of error (0.04)
Plugging in the values, we get:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2
n = 600.25
Rounding up to the nearest whole number, Jeremy will need a sample size of 601.
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suppose in an experiment, we randomly assign 15 participants to three treatment groups 1, 2, and 3 (with five participants per treatment). each of the three groups has received a different method of speed-reading instruction. a reading test is given and the number of words per minute is recorded for each participant. below is a table with the data collectedf) what is your conclusion about the population mean among the groups?
The null hypothesis for a one-way analysis of variance (ANOVA) is that there is no significant difference between the means of the groups, while the alternative hypothesis is that at least one group mean is significantly different from the others.
The null hypothesis (H0) for a one-way analysis of variance is that there is no significant difference in the mean of the dependent variable (number of words per minute) among the groups, and any observed differences are due to chance.
The alternative hypothesis (Ha) is that there is a significant difference in the mean of the dependent variable among the groups, and this difference is not due to chance. In other words, at least one of the groups has a different mean from the others.
Symbolically, the hypotheses can be expressed as:
H0: μ1 = μ2 = μ3 (where μ1, μ2, and μ3 are the population means for groups 1, 2, and 3, respectively)
Ha: At least one of the population means is different from the others.
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--The given question is incomplete, the complete question is given
" Suppose in an experiment, we randomly assign 15 participants to three treatment groups 1, 2, and 3 (with five participants per treatment). Each of the three groups has received a different method of speed-reading instruction. A reading test is given and the number of words per minute is recorded for each participant. Below is a table with the data collected:
Group 1 Group 2 Group 3
700 480 500
850 460 550
820 500 480
640 570 600
920 580 610
Write the null and alternative hypotheses for a one-way analysis of variance."--
pls help find the unknown angles
Answer:
x=34, z=26 degrees, y=74 degrees
Step-by-step explanation:
We can find x because the triangles are equal to each other, meaning that we can set 2x-20 equal to 4x-88. When solved, x=34. This now means that the expression 2x-20 and 4x-88 both equal to 48 degrees.
Now looking at the triangle on the left, we can find the angle using supplementary angles, setting 180-154, which is 26 degrees. This means z on the triangle to the right is also 26 degrees since the triangles are equal to each other.
Because of knowing two angles, we can now find the 3rd one by adding both of them up and subtracing it from 180. That will get you 106 degrees, then using vertical angles we can find that the angle measure of 106 degrees carries over to the second triangle.
To find y now, you simply subtract 106 from 180 to get 74 degrees.
(I believe this is right, hopefully it made sense!)
PLEASE ANSWER FAST!!!!!!!!!!!!!
B. The line of symmetry should have been 4 instead of –4.
We are given the quadratic:
, with a=1, b=-8, c=15.
and the quadratic equation is [tex]x^2[/tex]-[tex]8[/tex][tex]x[/tex]+[tex]15[/tex]=0
We know that the x-coordinate of the vertex, which is the point where the line of symmetry passes through is
.
Thus, the x-coordinate of the vertex is .
Thus, the line of symmetry is x=4.
A line of symmetry is a line that divides a shape into two equal parts that are mirror images of each other. It is also called a mirror line or axis of symmetry.
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Sp
4
A square has an area of 100 sq meters. What is the perimeter of the square?
The area of a square is given by the formula A = s^2, where s is the length of a side of the square. If the area of the square is 100 sq meters, then:
s^2 = 100
Taking the square root of both sides, we get:
s = 10
Therefore, the length of a side of the square is 10 meters. Since all four sides of a square are equal, the perimeter of the square is:
4s = 4(10) = 40 meters
A ball is thrown across the field from point A to point B. It hits the ground at point B. The path of the ball is shown in
the diagram below. The x-axis shows the horizontal distance the ball travels in feet, and the y-axis shows the height of
the ball in feet. Use the diagram to complete parts (a)-(f).
a.
b.
C.
d.
e.
f.
A
C
B
Suppose point A is approximately 6 feet above ground and that at time t=0 the ball is at point A. Suppose
the length of OB is approximately 88 feet. Include this information on the diagram.
Suppose that after 1 second, the ball is at its highest point of 22 feet (above point C) and has traveled a
horizontal distance of 44 feet. What are the approximate coordinates of the ball at the following values of
t: 0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, and 2.
Use your answer from part (b) to write two predictions.
What is happening to the ball when it has coordinates (88, 0)?
Why do you think the ball is at point (0, 6) when t = 0? In other words, why isn't the height of the ball 0?
Does the graph allow us to make predictions about the height of the ball at all points?
Based on the information, the height of point A is 6 feet above ground and the length of OB is approximately 88 feet.
How to explain the valueb) At t = 0.25 seconds, the approximate coordinates of the ball are (11, 13.5).
At t = 0.5 seconds, the approximate coordinates of the ball are (22, 12).
At t = 0.75 seconds, the approximate coordinates of the ball are (33, 9).
At t = 1 second, the approximate coordinates of the ball are (44, 6).
At t = 1.25 seconds, the approximate coordinates of the ball are (55, 3).
At t = 1.5 seconds, the approximate coordinates of the ball are (66, 0).
At t = 1.75 seconds, the approximate coordinates of the ball are (77, -3).
At t = 2 seconds, the approximate coordinates of the ball are (88, -6).
The height of the ball will be negative when it reaches point B again after traveling from A to B, assuming it follows the same path.
The time it takes for the ball to reach its maximum height and return to the ground will be approximately 2 seconds.
When the ball has coordinates (88, 0), it has reached the ground at point B, and its horizontal distance traveled is 88 feet.
At t = 0, the ball is at point A, which is 6 feet above the ground. This is because it was thrown from that height, and the time elapsed is not enough for gravity to affect its height yet.
Yes, the graph allows us to make predictions about the height of the ball at all points. However, the accuracy of the predictions may depend on the assumptions and approximations made about the ball's initial velocity, air resistance, and other factors.
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Adele read an article about how tax-payers completed the majority of their tax forms. Here is what the article stated:
Who completed forms Self Family or friend Professional
47
%
47%47, percent 12
%
12%12, percent 41
%
41%41, percent
She wondered if senior citizens in her community followed this distribution, so she surveyed a random sample of 200
200200 senior citizens about how they completed their taxes. Here are her results:
Who completed forms Self Family or friend Professional
Senior citizens 90
9090 21
2121 89
8989
She wants to use these results to carry out a χ
2
χ 2
\chi, squared goodness-of-fit test to determine if senior citizens in her community complete their taxes differently than the article suggests.
What are the values of the test statistic and P-value for Adele's test?
Answer: x^2 = 1.143;
P-value > 0.25
Step-by-step explanation: I got it right on khan academy!!
The P-value for the test is less than 0.05, indicating strong evidence against the null hypothesis. Adele can conclude that senior citizens in her community complete their taxes differently than what was reported in the article.
To carry out a χ2 goodness-of-fit test, Adele needs to compare the observed frequencies of how senior citizens completed their taxes with the expected frequencies based on the distribution reported in the article. The test statistic for this type of test is calculated as the sum of the squared differences between the observed and expected frequencies divided by the expected frequencies. In this case, the test statistic is 15.67. The degrees of freedom for the test are equal to the number of categories minus one, which in this case is 3 - 1 = 2. Using a significance level of 0.05, the critical value for the test is 5.99. Since the test statistic of 15.67 is greater than the critical value of 5.99, we reject the null hypothesis that the senior citizens in the community complete their taxes according to the distribution reported in the article.
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A senator wants to know her approval rating among the constituents in her state. She has her staff obtain 1000 responses to a telephone survey of
registered voters in her state
O Simple Random Sample
O Systematic
O Self-Selected
Convenience
O Stratefied
Answer:B
Step-by-step explanation:
of 346 cupcakes tested at tasty creme cupcake bakery , 12 are found to be defective and had no creme inside. construct the 98% confidence interval for the proportion of all cupcakes that have no creme filling.
The required proportion of cupcakes that have no creme filling with 98% confidence interval is equal to (0.012, 0.058).
Total number of cupcakes = 346
Number of defective cup cakes = 12
Confidence interval = 98%
To construct a confidence interval for the proportion of all cupcakes that have no creme filling,
Use the following formula,
CI = p ± z√((p(1-p))/n)
where,
p = proportion of defective cupcakes
n = sample size
z = z-value for the desired confidence level (98% in this case)
Plug in the values we have,
p = 12/346
= 0.0347
n = 346
z = 2.33 (from a standard normal distribution table for a 98% confidence level)
CI = 0.0347 ± 2.33√((0.0347(1-0.0347))/346)
= 0.0347 ± 0.023
So the 98% confidence interval for the proportion of all cupcakes that have no creme filling is (0.012, 0.058).
Therefore, 98% confidence interval that have true proportion of all cupcakes with no creme filling is between 0.012 and 0.058.
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Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to eleven mysteries and six nonfiction books. If she randomly chooses three books from her selections, what's the probability that they will all be mysteries? Enter a fraction or round your answer to 4 decimal places, if necessary.
the probability that Lindsay will choose three mystery books is 0.1141 or 1141/10,000 as a fraction.
What's the probability that they will all be mysteries?Lindsay has 11 mystery books and 6 nonfiction books. The probability of Lindsay choosing one of her mystery books first is 11/17. Once she has chosen one mystery book, there are 10 remaining, so the probability of her choosing another one is 10/16.
Finally, there are 9 mystery books remaining when she chooses her third book, making the probability of her choosing one of her mystery books 9/15.
Thus, the probability that Lindsay chooses three mystery books is:P(mystery book 1 AND mystery book 2 AND mystery book 3)
= P(mystery book 1) * P(mystery book 2| mystery book 1) * P(mystery book 3| mystery book 1 and book 2)
P(mystery book 1) = 11/17P(mystery book 2| mystery book 1)
= 10/16P(mystery book 3| mystery book 1 and book 2)
= 9/15
Therefore, P(mystery book 1 AND mystery book 2 AND mystery book 3) = (11/17) * (10/16) * (9/15)
= 0.1141 (rounded to four decimal places)
Thus, the probability that Lindsay will choose three mystery books is 0.1141 or 1141/10,000 as a fraction.
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sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represetns her situation?
A) linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
We know that Sarah was selling lemonade and she makes 0.50 dollars on a small cup, and 1 dollar on a medium cup but she wants to make at least 30 dollars and only has 75 cups.
We need to show a linear inequality where, 's' represents a small cup, and 'm' represents a medium cup:
Linear inequalities are the expressions where any two values are compared by the inequality symbols ‘<’, ‘>’, ‘≤’ or ‘≥’
Linear equations are a combination of constants and variables.
let number of small cups be s,
therefore, total amount of small cups = 0.5 s
let number of medium cups be m,
therefore, total amount of medium cups = 1 m
with this given information, we can form our equation as:
0.5 s + 1 m = 30 < 75.
Therefore, a linear inequality, 0.5 s + 1 m = 30 < 75 where, 's' represents a small cup, and 'm' represents a medium cup.
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Complete question: Sarah was selling lemonade. she makes .50 dollars on a small cup, and 1 dollar on a medium cup. She wants to make at least 30 dollars and only has 75 cups. If s represents a small cup, and m represents a medium cup, which system of linear inequalities correctly represents her situation?
A. 0.5 s + 1 m = 30 < 75
B. 1s + 3m + 5l
C. $75
D. $93
calcula valor exacto de E:
E = 3 √5 + 7 π/ 5 - 2 ( √5 - 3 π)
Answer: √5 + 37π/5.
Step-by-step explanation:
To calculate the exact value of E, we can follow the order of operations (PEMDAS):
E = 3√5 + 7π/5 - 2(√5 - 3π)
E = 3√5 + 7π/5 - 2√5 + 6π (distribute the -2)
E = (3√5 - 2√5) + (7π/5 + 6π) (combine like terms)
E = √5 + 37π/5
Therefore, the exact value of E is √5 + 37π/5.
I need help answering this question, please tell me how you got the answer
The properties of the conic section are Ellipse, Domain = [-2, 2] and the range is [-3, 3]
Identifying the properties of the conic sectionFrom the question, we have the following parameters that can be used in our computation:
The conic section
From the graph, we have
The conic section is an ellipse
The domain of this equation is all possible values of x and the range is for y
From the graph, we have
x values = -2 to 2
y values = -3 to 3
These are the domain and the range
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The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram
The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram contradicts the rule which states that the sum of all angles in any quadrilateral is 360°.
What is a quadrilateral?
The Latin words quadra refers to number four, and latus refers to the sides, on combining gives quadrilateral. Any polygon with four sides, four angles, and four corners is said to be a quadrilateral. It is a closed shape known as a quadrilateral which is formed by joining any four points, any three of these points must not be on a same line.The quadrilateral has interior angles at each of its four corners. The sum of all for interior angles is always 360°.
Given that The sum of an angle measures of any trapezoid is greater than the sum of the angle measures of any parallelogram:
As we know that trapezoid and parallelogram both are quadrilaterals. so both will have interior angles sum equal to 360°
The given statement is false.
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math smarties needed!
Answer:
1. [tex]y = (x + 2)(x + 3)[/tex]
2. [tex]y = -x(x + 4)[/tex]
Step-by-step explanation:
We can find the factored form of the graphed quadratic functions by:
1) Expressing each one in vertex form
2) Expanding and refactoring to rewrite in factored form
1. We know that vertex form is:
[tex]y = a(x-h)^2 + k[/tex],
where [tex]a[/tex] determines the parabola's direction and width ([tex]a=1[/tex] being the same as a standard parabola), and [tex](h,k)[/tex] is the parabola's vertex.
The vertex of this parabola is (-3, -4).
↓ plugging these values into the vertex form equation
[tex]y = 1(x - (-3))^2 + (-4)[/tex]
↓ simplifying
[tex]y = (x + 3)^2 - 4[/tex]
Now, we can expand and refactor this equation into factored form.
↓ expanding the squared term
[tex]y = (x^2 + 6x + 9) - 4[/tex]
↓ simplifying
[tex]y = x^2 + 6x + 5[/tex]
↓ factoring
[tex]\boxed{y = (x + 2)(x + 3)}[/tex]
2. We can see that the vertex is at (-2, 4).
↓ plugging into the vertex form equation
[tex]y = -1(x - (-2))^2 + 4[/tex]
Note that the parabola opens downward, so [tex]a = -1[/tex].
↓ simplifying
[tex]y = -1(x +2)^2 + 4[/tex]
↓ expanding the squared term
[tex]y = -1(x^2 +4x + 4) + 4[/tex]
↓ incorporating the outer +4 into the distribution of -1
[tex]y = -1(x^2 + 4x + 4 - 4)[/tex]
↓ simplifying
[tex]y = -1(x^2 + 4x)[/tex]
↓ factoring
[tex]y = -1(x)(x + 4)[/tex]
↓ simplifying
[tex]\boxed{y = -x(x + 4)}[/tex]
A meal costs $5.75. You offer a 10% discount. The sales tax is 4%. How much should you charge the customer? $
Answer:
To calculate the final cost of the meal, we need to first calculate the discount and then add the sales tax. Discount = 10% of $5.75 = $0.575 Price after discount = $5.75 - $0.575 = $5.175 Sales tax = 4% of $5.175 = $0.207 Final cost = Price after discount + Sales tax = $5.175 + $0.207 = $5.382 Therefore, you should charge the customer $5.382.
well, let's hmmm apply the 10% discount first
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10\% of 5.75}}{\left( \cfrac{10}{100} \right)5.75} ~~ \approx ~~ 0.58~\hfill \stackrel{ 5.75~~ - ~~0.58 }{\approx\text{\LARGE 5.17}}[/tex]
now let's apply the 4% tax to it
[tex]\stackrel{\textit{4\% of 5.17}}{\left( \cfrac{4}{100} \right)5.17} ~~ \approx ~~ 0.21\hspace{5em}\stackrel{ 5.17~~ + ~~0.21 }{\text{\LARGE 5.38}}\qquad \textit{final charge}[/tex]
The solution to 15 + a2 − 1 = 5 2a − 2 is a =___. The extraneous solution is a =____.
The solution to the equation is a = 6 and a = 4.
There is no extraneous solution.
To find the solution for the given equation, follow these steps:
1. Rewrite the equation: [tex]15 + a^2 - 1 = 5(2a - 2)[/tex].
2. Simplify both sides: [tex]a^2 + 14 = 10a - 10.[/tex]
3. Move all terms to one side:[tex]a^2 - 10a + 24 = 0.[/tex]
4. Factor the quadratic equation: (a - 6)(a - 4) = 0.
5. Set each factor equal to zero: a - 6 = 0 or a - 4 = 0.
6. Solve for 'a': a = 6 or a = 4.
Now, we need to check if both solutions are valid or if there is an extraneous solution.
Since there are no restrictions on the domain of the original equation, both solutions are valid.
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HEEEEEEEELLLLLLLLLLPPPPPPPPP!!!!!!!!!
Answer:
The horizontal translation of the function is 3 units to the right (from the parent function). Therefore, we subtract 3 from the x-value of the function.
The equation of the graphed function in vertex form is:
[tex]\boxed{y = (x - 3)^2- 2}[/tex]
Step-by-step explanation:
The given graph shows a parabola that opens upwards.
Therefore, the equation for this function is a quadratic equation with a positive leading coefficient.
The vertex of a parabola is the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.
From inspection of the given graph, the vertex of the function is (3, -2).
The parent function of a parabola that opens upwards is y = x². This has a vertex at (0, 0).
Therefore, given the vertex of the given function is (3, -2), the parent function has been translated 3 units right and 2 units down.
For a horizontal translation to the right, we subtract the number of units from the x-value of the function.
For a vertical translation down, we subtract the number of units from the function.
Therefore, a translation of 3 units right and 2 units down from the parent function y = x² is:
[tex]\boxed{y = (x - 3)^2- 2}[/tex]
This function is written in vertex form.
To write the equation in standard form, expand the brackets and simplify:
[tex]\implies y=(x-3)(x-3)-2[/tex]
[tex]\implies y=x^2-3x-3x+9-2[/tex]
[tex]\implies y=x^2-6x+7[/tex]
[tex]\hrulefill[/tex]
Additional comments
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex. Therefore, the "k" value refers to the y-value, which is the vertical translation from the parent function.
As your question refers to the "k" value for the horizontal translation, we assume that it is not referring to the k-value of the vertex form.
which of the below statements are true? i. probability is usually between 0 and 1, inclusive. ii. an event that is likely has a probability that is close to 1. iii. an event that is likely has a probability that is close to 0. iv. an event that is unlikely has a probability that is close to 1. v. an event that is unlikely has a probability that is close to 0.
The true statements are
i. probability is usually between 0 and 1, inclusive.
ii. an event that is likely has a probability that is close to 1.
(option i and ii).
Probability is an important concept in mathematics and statistics that allows us to quantify the likelihood or chance of an event occurring. It is often represented as a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain to occur.
Now, let's examine each of the statements to determine which ones are true.
The first statement, "probability is usually between 0 and 1, inclusive," is true. As mentioned earlier, probability is always represented as a number between 0 and 1, inclusive.
The second statement, "an event that is likely has a probability that is close to 1," is also true. If an event is likely to occur, it means that there is a high probability of it happening. Therefore, the probability assigned to that event would be close to 1.
Hence the correct option is (a) and (b)..
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Susan rolled a die 702 times. Which of the following would be a good estimate of the number of times she rolled the number 3 on the die?
Times Rolled: 702
Need estimation of: 3
Numbers on the dice: 6
702/6 = 117
Answer: 117
Solve the expression one-half x (48 ÷ 6) – 2 + 5 using PEMDAS.
7
8
9
10
The value of the expression using PEDMAS is 7.
What is PEDMAS?The acronym PEMDAS, which can alternatively stand for "Please Forgive My Dear Aunt Sally," is a mnemonic tool for remembering the order of operations in mathematical and algebraic formulas. Its acronym is:
P - Parenthesis (operations inside parentheses are done first)
E: Exponents (operations involving exponents are done next)
Divide and multiply is abbreviated MD (these operations are done left to right, whichever comes first)
AS stands for addition and subtraction (these operations are done left to right, whichever comes first). No matter how they approach it or how they understand it, PEMDAS helps to ensure that the same statement is assessed in the same way by various people. In mathematics, it is crucial to understand this idea, especially when working with complicated expressions or formulae.
The given expression is 1/2 x (48 ÷ 6) – 2 + 5.
Simplifying the expressions we have:
1/2 x (48 ÷ 6) – 2 + 5
= 1/2 x 8 - 2 + 5
= 4 - 2 + 5
= 7
Hence, the value of the expression using PEDMAS is 7.
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solve[tex]\sqrt{-4=4[/tex]
The radical expression √(-4x) = 4 when evaluated has a value of x = -4
Evaluating the radical expressionFrom the question, the equation is given as
√(-4x) = 4
We can start by squaring both sides of the equation to eliminate the square root:
(√(-4x))^2 = 4^2
So, we have
-4x = 16
Dividing both sides by -4, we get:
x = -4
However, we need to check if this solution satisfies the original equation.
√(-4x) = √(-4(-4)) = √(16) = 4
So, the only solution to the equation is x = -4.
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