Answer:
( x + 3)² + ( y + 7)² = 361
Step-by-step explanation:
The equation of a circle written in standard form is ( x – h)² + ( y - k)² = r². The center is (h, k) and the radius is r.
With the given information of center (-3, -7) and radius 19, we get
[ x – (-3)]² + [ y - (-3)]² = (19)²
( x + 3)² + ( y + 7)² = 361
20 = r + 11
Solve the equation.
Answer: r = 9
Step-by-step explanation:
Simplifying
20 = r + 11
Reorder the terms:
20 = 11 + r
Solving
20 = 11 + r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-1r' to each side of the equation.
20 + -1r = 11 + r + -1r
Combine like terms: r + -1r = 0
20 + -1r = 11 + 0
20 + -1r = 11
Add '-20' to each side of the equation.
20 + -20 + -1r = 11 + -20
Combine like terms: 20 + -20 = 0
0 + -1r = 11 + -20
-1r = 11 + -20
Combine like terms: 11 + -20 = -9
-1r = -9
Divide each side by '-1'.
r = 9
Simplifying
r = 9
Answer:
r=9
Step-by-step explanation:
Step 1: Flip the equation
r + 11 = 20
Step 2: Subtract 11 from both sides
r + 11 - 11 = 20 - 11
The distribution of the scores on a standardized math exam in a school district is skewed to the right. Which of the following statements is true about this distribution? Please hurry it is a timed test
Answer:
If the distribution is skewed right, then the mode is greater than the mean.
Step-by-step explanation:
There's a graph below that I hope will help!
The true statement is that the mode of the scores is greater than the mean score
How to determine the true statement?From the question, we understand that:
The distribution is skewed to the right
For a right skewed distribution, the mean value is lesser than the mode value
i.e. mean < mode or mode > mean
Hence, the true statement is that the mode of the scores is greater than the mean score
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A pizza chain records how long it takes customers to receive their delivery orders. Suppose the distribution of these delivery times is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 10 minutes. Management plans on calculating the mean delivery time from a random sample of 25 orders. We can assume independence between orders in the sample.
What is the probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean?
Answer:
The probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean cannot be calculated.
Step-by-step explanation:
As given in the question statement, the distribution of delivery times is strongly skewed to the right. The population distribution is skewed to right. Too much skewed distribution can cause the statistical model to work ineffectively and affects its performance. The probability can also not be calculated because the sample size is too small. Small sample size affects the results and makes them less reliable because it results in a higher variability and likelihood of skewing the results.
Answer:
We cannot calculate this probability because the sampling distribution is not normal.
Step-by-step explanation:
Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.
A hypothesis test was used to see if less than 5% of all Americans would still drive to work if gas prices went above $10.00 a gallon. The P-value for this test was 0.03. We can conclude that only 3% of all Americans would still drive to work if gas prices went above $5.00.True / False.
Answer:
The correct option is;
False
Step-by-step explanation:
Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03
The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.
Help please
This question is stressing me out
Answer:
Maximum: C= 6(5) + 2y or C= 30 + 2y
Step-by-step explanation:
X can be greater than or equal to 0, but can also be less than or equal to 5.
Y is greater than or equal to 0.
4 times x then subtracted by y is greater than or equal to 1.
Since X can't go higher than 5, the maximum is 5.
Y can be anything since it can be greater than or egual to 0 and either way it would be greater than one.
I hope I could help!
For what values of x is x2-36=5x true?
Answer:Its B. -4 and 9
Step-by-step explanation:
Answer:
x = - 4, x = 9
Step-by-step explanation:
Given
x² - 36 = 5x ( subtract 5x from both sides )
x² - 5x - 36 = 0 ← in standard form
Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)
The factors are - 9 and + 4, since
- 9 × 4 = - 36 and - 9 + 4 = - 5, thus
(x - 9)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 9 = 0 ⇒ x = 9
While playing a trivia game Adam answer eight questions correct in the first half and two questions correct in the second half if each question was worth eight points what's his final score
Answer:
80 points
Step-by-step explanation:
First Half: Second Half: Total Right Answers
8 questions right + 2 questions right = 10 questions right
10*8 points a piece = 80 points
Thus, his total score is 80 points.
To find Adam's final score, we need to calculate the total points from both the first and second halves of the trivia game. Each question is worth 8 points.
First HalfAdam answered 8 questions correctly:
8 questions × 8 points per question = 64 points
Second HalfAdam answered 2 questions correctly:
2 questions × 8 points per question = 16 points
Total ScoreNow, we add the points from both halves:
First half: 64 pointsSecond half: 16 pointsTotal Score = 64 points + 16 points = 80 points
Therefore, Adam's final score in the trivia game is 80 points.
compare 9 X 10^4 to 3 X 10^2
Step-by-step explanation:
[tex]9 \times {10}^{4} = 900 \times {10}^{2} \\ \\ 3 \times {10}^{2} \\ \\ \because \: 900 > 3 \\ \purple{ \boxed{ \bold{\therefore \: 9 \times {10}^{4} > 3 \times {10}^{2}}}}[/tex]
SAT Scores 1510 1480 2100 1800 1300 1250 1400 1430 1390 1520 The SAT scores for a group of 10 students are shown. What is the mean absolute deviation of the group (round to the nearest tenth)
The mean absolute deviation of the group of SAT scores is approximately 169.8.
To find the mean absolute deviation (MAD) of the group of SAT scores, we follow these steps:
1. Calculate the mean (average) of the scores.
2. Find the absolute deviation of each score from the mean.
3. Calculate the mean of these absolute deviations.
Let's proceed with the calculations:
1. Calculate the mean:
[tex]\[ \text{Mean} = \frac{1510 + 1480 + 2100 + 1800 + 1300 + 1250 + 1400 + 1430 + 1390 + 1520}{10} \][/tex]
[tex]\[ \text{Mean} = \frac{14,580}{10} \][/tex]
[tex]\[ \text{Mean} = 1458 \][/tex]
2. Find the absolute deviation of each score from the mean:
[tex]\[ \text{Absolute deviations: } |1510 - 1458| = 52, |1480 - 1458| = 22, |2100 - 1458| = 642, |1800 - 1458| = 342, \][/tex]
[tex]\[ |1300 - 1458| = 158, |1250 - 1458| = 208, |1400 - 1458| = 58, |1430 - 1458| = 28, |1390 - 1458| = 68, |1520 - 1458| = 62 \][/tex]
3. Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{52 + 22 + 642 + 342 + 158 + 208 + 58 + 28 + 68 + 62}{10} \][/tex]
[tex]\[ \text{MAD} = \frac{1698}{10} \][/tex]
[tex]\[ \text{MAD} = 169.8 \][/tex]
Therefore, the mean absolute deviation of the group of SAT scores is 169.8 (rounded to the nearest tenth).
The mean absolute deviation of the group of SAT scores is 162 (rounded to the nearest tenth).
To find the mean absolute deviation (MAD) of a set of data, you first need to calculate the mean (average) of the data, then find the absolute difference between each data point and the mean, and finally, calculate the average of these absolute differences.
Calculate the mean of the given SAT scores: (1510 + 1480 + 2100 + 1800 + 1300 + 1250 + 1400 + 1430 + 1390 + 1520) / 10 = 14660/10
= 1466
Calculate the absolute deviation of each score from the mean: |1510 - 1466|, |1480 - 1466|, and so on.
This gives - 44+14+634+334+166+216+66+36+76+54
= 1620
Calculating MAD -
= 1620/10
= 162
The mean absolute deviation of the group of SAT scores is 162 (rounded to the nearest tenth).
i need help with rhombus,rectangles and squares
Answer:
a= 11, b= 12
Opposite angles of parallelogram are equal.
m<D = m<B
9b-2=106°
9b= 108°
b= 12°
Sum of the adjacent angles of a parallelogram = 180°
m<B+m<C = 180°
106°+7a-3=180°
7a = 180°-106°+3
7a=77°
a= 11°
An item that regularly sells for $425 is marked down to $318.75. What is the
discount rate?
Answer: 25%
Step-by-step explanation:
[tex]\frac{425}{318.75}=\frac{100}{x}[/tex]
[tex]x=\frac{(318.75*100)}{425}\\x=75[/tex]
100-75=25
You buy a ticket to the Warriors game for $409.20. You get the ticket and it says the
cost was originally sold for $62. What was the markup?
Which triangle shows the incenter at point A?
The Images are placed in order A- D
Answer:
B
Step-by-step explanation:
the incenter is found by constructing angle bisectors and then intersecting the three angle bisectors.
A 1,127-foot tree has grown at a constant rate each year. In the equation below, t is the age of the tree in years.
23t = 1,127
What is the unit rate in the equation above?
Answer:
Your answer will be 17
Step-by-step explanation:
Simply multiply and take away the t and add into the 9+ after your equation
HELP FAST PLZ I HAVE LITTLE TIME I DONT WANT TO FAIL.
Given:
Given that the diameter of the circle is [tex]\frac{7}{2} \ cm[/tex]
We need to determine the radius, circumference in terms of π and circumference using π = 3.14.
Radius:
The radius of the circle can be determined using the formula,
[tex]r=\frac{d}{2}[/tex]
Substituting [tex]d=\frac{7}{2}[/tex], we get;
[tex]r=\frac{(\frac{7}{2})}{2}}[/tex]
Simplifying, we get;
[tex]r=\frac{7}{4} \ cm[/tex]
Thus, the radius of the circle is [tex]\frac{7}{4} \ cm[/tex]
Circumference in terms of π:
The circumference of the circle can be determined using the formula,
[tex]C=2 \pi r[/tex]
Substituting [tex]r=\frac{7}{4} \ cm[/tex], we get;
[tex]C=2 \pi (\frac{7}{4})[/tex]
[tex]C=\frac{7}{2} \pi \ cm[/tex]
Thus, the circumference in terms of π is [tex]\frac{7}{2} \pi \ cm[/tex]
Circumference using π = 3.14:
Substituting π = 3.14 in the circumference of the circle [tex]C=\frac{7}{2} \pi \ cm[/tex], we get;
[tex]C=\frac{7}{2}(3.14)[/tex]
[tex]C=10.99 \ cm[/tex]
Thus, the circumference of the circle is 10.99 cm
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
Answer:
C. f(x)=5x^2-4x+5 is the correct answer on edge 2021
What’s 20 times 1000
to answer this it's simple
the answer is 20,000
PLEASE HELP! Which statements are true about three-dimensional figures? Select two options.
A) A sphere has no bases.
B) A prism must have a triangular or rectangular base.
C) A square pyramid must have lateral faces that are squares.
D) A triangular prism has two triangular bases and four triangular lateral faces.
E) The lateral face of a cylinder is in the shape of a rectangle.
Answer:
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
The correct statements which are true about three-dimensional figures are,
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
To find correct statements which are true about three-dimensional figures.
Now, We know that;
In a sphere, it has no base.
And, In a cylinder, The lateral face is in the shape of a rectangle.
Thus, The correct statements which are true about three-dimensional figures are,
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
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Solve the system of equations. -10y+9x=-9
10y+5x=-5
by the use of elimination method
make all coefficients of subject to be eliminated similar..by multiplying the coefficients with one another
for eqn(i)
5(-10y+9x=-9)
-50y+45x=-45
for eqn(ii)
9(10y+5x=-5)
90y+45x=-45
-50y+45x=-45
90y+45x=-45
...subtract each set from the other...
we get
-140y+0=0
y=0
from eqn(i)
10y+5x=-5
0+5x=-5
x= -1
A class of 25 students shares a class set of 100 markers. On a day with 5 students absent, which statement is true?
A
For every 5 students, there is 1 marker.
B
For every 4 students, there is 1 marker.
C
For each student, there are 4 markers.
D
For each student, there are 5 markers.
Answer:
D
Step-by-step explanation:
Answer:
D. For each student, there are 5 markers.
Step-by-step explanation:
A class of 25 students shares a set of 100 markers.
5 students are absent.
Therefore,
No. of students present = 25 - 5 = 20
No. of markers = 100
No. of markers each student gets = 100/20 = 10/2 = 5
Hence, each student gets 5 markers.
The expression 15p+12r shows the total cost of buying p printed shirts and r plain shirts find the total cost if you buy two printed shirts and three plain shirts
In Mathematics, we use algebraic expressions to solve problems. In this case, substituting the numbers of printed and plain shirts into the given expression determines the total cost, which is 66.
Explanation:The subject of this question is in the discipline of Mathematics, specifically within algebraic expressions. The expression representing the total cost of buying shirts is 15p+12r, where p is the number of printed shirts and r is the number of plain shirts.
To find the total cost for buying two printed shirts and three plain shirts, we substitute p with 2 and r with 3 in the given expression.
So, the total cost becomes: 15*2 + 12*3 = 30 + 36 = 66. Therefore, the total cost of buying two printed shirts and three plain shirts is 66.
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Final answer:
The total cost of buying two printed shirts and three plain shirts can be calculated by substituting into the expression 15p + 12r. The result is a total cost of $66.
Explanation:
The student is asking how to calculate the total cost of buying printed and plain shirts. The expression to find the total cost is given as 15p + 12r, where p is the number of printed shirts and r is the number of plain shirts. To find the total cost for two printed shirts and three plain shirts, we substitute p with 2 and r with 3 into the expression, which gives us:
Total Cost = 15(2) + 12(3)
Total Cost = 30 + 36
Total Cost = 66
Therefore, if you buy two printed shirts and three plain shirts, the total cost would be $66.
The High Roller wheel in Las Vegas has a diameter of 520 feet and its base is 30 feet off the ground. You board a gondola on the wheel and rotate 240 degrees counterclockwise before the wheel temporarily stops. How high above the ground are you when the wheel stops?
Answer:
420 feet
Step-by-step explanation:
GIVEN: The High Roller wheel in Las Vegas has a diameter of [tex]520[/tex] feet and its base is [tex]30[/tex] feet off the ground. You board a gondola on the wheel and rotate [tex]240[/tex] degrees counterclockwise before the wheel temporarily stops.
TO FIND: How high above the ground are you when the wheel stops?
SOLUTION:
Consider the figure attached.
As wheel rotate counter clockwise [tex]240^{\circ}[/tex], its current position is [tex]120^{\circ}[/tex] clock wise.
Total height [tex]=260+30+h\rightarrow290+h[/tex]
Calculating value of [tex]h[/tex]
[tex]\sin 30^{\circ}=\frac{h}{260}\impliesh=260\sin30^{\circ}[/tex]
[tex]\implies h=260\times\frac{1}{2}=130feet[/tex]
Total height [tex]=290+130[/tex] feet
[tex]=420\text{ feet}[/tex]
Hence total height is 420 feet
Find the domain of the following function:
y = x^3 − 8
________
x^2 + 5x + 6
Select the appropriate response:
A) domain: x cannot equal −3, −2
B) domain: x equals −3, −2
C) None of the above
Help please! 40 points!
Answer:
The answer is C.
Step-by-step explanation:
You can do it by solving both equations :
y = x³ - 8
Let y=0,
x³ - 8 = 0
x³ = 8
x = ³√8
= 2
x² + 5x + 6 = 0
(x+3)(x+2) = 0
x = -3
x = -2
So the domain for 1st equation is 2 and 2nd equation is -2 & -3.
In 1st equation, the answer cannot be option A & B and in 2nd equation, the answer is B.
Answer:
A) domain: x cannot equal −3, −2
Step-by-step explanation:
y = x^3 − 8
________
x^2 + 5x + 6
The function is undefined when the denominator goes to zero
x² + 5x + 6 = 0
x² + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
(x + 2)(x + 3) = 0
x = -3, -2
Domain can take any value except -2 and -3
Jared made 4 bird houses in 3 days. How many days will work to make 20 bird houses?
Answer:
15 days
Step-by-step explanation:
We can use a ratio to solve
4 bird houses 20 bird houses
--------------------- = -------------------------
3 days x days
Using cross products
4x = 3*20
4x = 60
Divide each side by 4
4x/4 = 60/4
x = 15
15 days
Answer:
15 days
Step-by-step explanation:
i hope this help you
Solve the following expressions:
1. 3² + 4²
2. 2² + 5²
3. 10² - 8²
4. √81
5. √144
6. √225
Step-by-step explanation:
3² + 4² = 9 + 16 = 252² + 5² = 4 + 25 = 2910² - 8² = 100 - 64= 36√81 = √9² = 9√144= √12² = 12√225 = √15² = 15Hope it will help you :)
Which value of x satisfies the equation?
1.6+x=4.8
Answer:
x=3.2
Step-by-step explanation:
This question is asking us to solve for x, and to do that, we need to get the variable by itself.
1.6+x=4.8
Subtract 1.6 from both sides
1.6-1.6+x=4.8-1.6
x=3.2
So, 3.2 is the value of x that satisfies the equation.
To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four-digit code. If repetition of the same four digits is not allowed (for example 5555), how many possible combinations are there?
Final answer:
The number of possible four-digit PIN combinations for an ATM, where no repetition of the same four digits is allowed, is 5040. This is calculated by multiplying the number of choices for each digit position, which are 10, 9, 8, and 7 respectively.
Explanation:
Calculating ATM PIN Code Combinations
To determine the number of possible four-digit PIN combinations for an ATM that does not allow the repetition of the same four digits (such as 5555), we have to consider how many choices we have for each digit. Since there are 10 possible digits (0-9) for each placement and repetition of the same four digits is not allowed, the first digit can be any of the 10 digits, the next digit can also be any of the 10 digits (except for the first digit), and so on.
The number of combinations can be calculated using factorial notation. For the first digit, there are 10 possibilities. For the second digit, there are 9 remaining possibilities (since the digit cannot be the same as the first), for the third digit, there are 8 possibilities, and for the fourth digit, there are 7 possibilities.
The calculation then becomes 10 x 9 x 8 x 7, which equals 5040 possible combinations. This shows that there are numerous ways to create a unique four-digit code without repeating the same digit four times.
Which concept is used to prove that the opposite sides of a parallelogram are congruent?
congruent rectangles
similar rectangles
congruent triangles
similar triangles
1 Intro
Done
Answer:
congruent triangles
Step-by-step explanation:
You can eliminate useless answers based on their wording. "Similar" anything cannot be used to prove congruence. "Rectangles" will not help you prove congruence of parallelogram sides. The only reasonable choice is ...
congruent triangles
_____
Typically, a diagonal is drawn through the figure, and the two triangles created are shown to be congruent, often by ASA. Then, by CPCTC, sides of the parallelogram are shown to be congruent.
Answer: congruent
Step-by-step explanation:
A researcher wishes to estimate, with 95% confidence, the proportion who own a laptop. A previous study shows that 70% of those interviewed had a laptop computer. How large a sample should the researcher select so that the estimate will be within 3% of the true proportion?
Answer:
The sample needs to be at least n = 897 in size.
Step-by-step explanation:
Given
Confidence Level = 95%
Let p = those who had laptop
p = 70% = 0.7
Margin of Error = 3% = 0.03
Let n = required sample.
To estimate the proportion of laptop owners with 95% confidence, first the z-value is calculated. [tex]z_{(a/2)}[/tex]
Given that confidence level = 95%
α = 1 − 95 %
α = 1 − 0.95
α = 0.05
So;
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.05/2)}[/tex]
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.025)}[/tex]
From the z table
[tex]z_{(0.025)} = 1.96[/tex]
Using formula for margin of error
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
where p + q =1
q = 1 - p
q = 1 - 0.7
q = 0.3
So,
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
[tex]0.03 = 1.96 * \sqrt{\frac{0.7 * 0.3}{n} }[/tex] --- Make n the subject of formula
First, square both sides
[tex]0.03^{2} = 1.96^{2} * {\frac{0.7 * 0.3}{n} }[/tex] ------ Multiply both sides by [tex]{\frac{n}{0.03^{2}}}[/tex]
[tex]0.03^{2} * {\frac{n}{0.03^{2}}} = 1.96^{2} * {\frac{0.7 * 0.3}{n} } * {\frac{n}{0.03^{2}}}[/tex]
[tex]n = 1.96^{2} * {\frac{0.7 * 0.3}{0.03^{2}} }[/tex]
[tex]n = {\frac{0.806736}{0.0009} }[/tex]
[tex]n = 896.473[/tex]
Hence, the sample needs to be at least n = 897 in size.
Like charges repel and unlike charges attract. Coulomb’s law states that the force F of attraction or repulsion between two charges, q1 and q2 is given by F= kq1q2/f^2, where k is constant and r is the distance between the positive charges. Suppose you were to graph F as a function of r for two positive charges
Coulomb's law explains the force between two charges. The force between two identical charges decreases as the distance between them increases. If graphed, this relationship will form a hyperbola.
Explanation:In physics, particularly electromagnetism, Coulomb's law explains the force between two charges. As per the law, the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the equation, F = kq1q2/r^2. Here, k is Coulomb's constant.
From this formula, we can conclude that force is inversely proportional to the square of the distance between two charges. In other words, as the distance (r) between two identical positive charges increases, the force (F) of repulsion between them decreases.
If we were to graph F as a function of r for two positive charges, the graph would be a hyperbola. This is because the equation represents an inverse square relationship. The force will decrease rapidly as the distance increases and is indicated by a curve that starts high when r is small and approaches zero as r gets larger.
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