If f(x) = 10 - 4x...
f(18) = 10 - 4(18) = 10 - 72 = -62 ≠ -2
This rules out answer a, since (18,-62) would be a point, not (18,-2).
f(-18) = 10 - 4(-18) = 10 + 72 = 82 ≠ -2
This rules out answer b, since (-18,82) would be a point, not (-18,2).
f(-2) = 10 - 4(-2) = 10 + 8 = 18
Answer c seems to be ok so far, since (-2,18) is a point in answer c.
f(2) = 10 - 4(2) = 10 - 8 = 2 ≠ =18
This rules out answer d, since (2,2) would be a point, not (2,-18).
The only answer that wasn't ruled out by check the first point in each answer is answer C.
A company uses paper cups shaped like cones for its water cooler. Each cup has a height of 8cm, and the base has a radius of 3cm . How much water is needed to fill 225 cups?
Please help me for brainiest !
The residuals for data set A and data set B were calculated and plotted on separate residual plots. If the residuals for data set A do not form a pattern, and the residuals for data set B form a pattern, what can be concluded?
A. Data set A is linear, and data set B is not linear.
B. Data set A is not linear, and data set B is not linear.
C. Data set A is linear, and data set B is linear.
D. Data set A is not linear, and data set B is linear.
The answer is B. Data set A in not linear, and data set B is not linear.
Find the combined volume of the composite figure. Use pl = 3.14
Round each volume to the nearest tenth. Then round your final answer to the nearest tenth.
Volume:
9 cm
6 cm
6.5 cm
cm³.
The volume of the solid given is 1073.88 cm³.
Given is a composite solid made up of a cone and a cylinder,
We need to find the volume of the composite solid,
So, to find the same we will add both volumes of both the solids,
V(cylinder) = π × radius² × height
V(cone) = π × radius² × height / 3
So, the volume =
= 3.14 × 6² × 6.5 + 3.14 × 6² × 9/3
= 3.14(6² × 6.5 + 6² × 3)
= 3.14(234 + 108)
= 3.14 × 342
= 1073.88 cm³
Hence the volume of the solid given is 1073.88 cm³.
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a neon light flashes five times every 10 seconds. Show that the light flashes 43,200 times in one day
a cube is inscribed in a sphere of radius 6. what is the volume of the cube? exact answer only. no decimal approximations.
The volume of the inscribed cube is equal to twice the cube of the sphere's radius, which is 864 cubic units.
Let the side of the inscribed cube be 's.' The diagonal of the cube is the diameter of the sphere, which is 12 units. Therefore, by using the Pythagorean theorem, we get:
s² + s² + s² = 12²
3s² = 144
s² = 48
The volume of the cube is given by s³, which is 48√3 cubic units.
Now, the volume of the sphere is (4/3)πr³, where r is the radius of the sphere. Since the sphere is inscribed in the cube, the diameter of the sphere is equal to the diagonal of the cube, which is s√3. Hence, r = (s√3)/2.
Substituting the value of r in the volume formula, we get:
(4/3)π[(6)(√3)/2]³ = (4/3)π(54√3) = 72π√3 cubic units
Therefore, the volume of the cube is twice the volume of the sphere, which is 864 cubic units.
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Use the commutative property to find the equal expression for each addition or multiplication expression
5 x 7
10 + 24
3 x 1
7 x 5
Answer:
Shown below.
Step-by-step explanation:
What is commutative property?The commutative property is a property of binary operations that states that the order of the operands does not affect the result of the operation. In other words, if you swap the order of the operands, you will still get the same result. This property holds true for addition and multiplication but not for subtraction and division.
So, 5 × 7 can be swapped to make it 7 × 5.10 + 24 can be swapped to make it 24 + 10.3 × 1 can be swapped to make it 1 × 3.7 × 5 can be swapped to make it 5 × 7, which is the same as the first expression.Therefore, the equivalent expressions in order are 7 × 5, 24 + 10, 1 × 3 and 5 × 7.
Imagine you have the following results from a case-control study, stratified on two levels of some characteristic:
Stratum 1 OR = 0.333
Stratum 2 OR = 0.335
Crude OR = 0.334
These results are most consistent with the characteristic being
Select one:
a. Neither a confounder nor an effect modifier
b. A confounder, but not an effect modifier
c. An effect modifier
d. A bias
The correct answer to the question is option c) An effect modifier.
A case-control study is a type of observational study that compares two groups of individuals: those who have the disease or outcome under investigation (cases) and those who do not (controls).
It aims to determine if an exposure or risk factor is associated with the development of the disease or outcome.
In this case, the results of the study indicate that there is a difference in the odds ratio (OR) between the two strata, which suggests that the characteristic being studied is an effect modifier.
An effect modifier is a factor that modifies the effect of the exposure on the outcome and leads to different measures of association across different levels of the factor.
Therefore, the characteristic is an effect modifier as it leads to different ORs in the two strata.
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kevin and nina are competing in a bike race. when kevin is ninety miles into the race, he is in first place. Nina is in second place and is 15 miles behing kevin. From this point, kevin contuines the race at a constant rate of 25mph and nina contuines the race at a constant rate of 30mph. When will nina catch kevin?
Nina will catch up Kevin in 1 hour.
Given that Kevin has completed 90 miles in the race and Nina completed 15 miles less, Kevin continues the race at a constant rate of 25mph and Nina continues the race at a constant rate of 30mph.
So, Nina covered the distance = 90-15 = 75 miles.
So,
When will finish the race, Kevin has already covered 15 miles,
So, Nina needs to catch Kevin by covering 15 + 15 = 30 miles
So, time taken by Nina cover 30 miles = 30/30 = 1 hours
Hence Nina will catch up Kevin in 1 hour.
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helpppppp pleaseeeee
Answer:
[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]
[tex]\alpha = 1 \quad \textsf{and} \quad \beta=2[/tex]
[tex]b=-3[/tex]
Step-by-step explanation:
If α and β are roots of x² + bx + c = 0 then the equation must be:
[tex](x -\alpha)(x - \beta) = 0[/tex]
Expanding we get:
[tex]x^2-\beta x - \alpha x + \alpha \beta = 0[/tex]
[tex]x^2-(\alpha +\beta ) x + \alpha \beta = 0[/tex]
Equating the coefficients we get:
[tex]\alpha + \beta=-b[/tex]
[tex]\alpha \cdot \beta=c[/tex]
For an equation with the roots α³ and β³, the sum of the roots can be rewritten in terms of (α + β) and (α·β) using the Sum of Cubes formula, and the Square of Binomials formula:
[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)(\alpha^2-\alpha\beta+\beta^2)\\&=(\alpha + \beta)(\alpha^2+2\alpha\beta+\beta^2-3\alpha\beta)\\&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\end{aligned}[/tex]
Substitute in the expressions for (α + β) and αβ to find the sum of the roots α³ and β³ in terms of b and c:
[tex]\begin{aligned}\alpha^3+\beta^3&=(\alpha + \beta)((\alpha+\beta)^2-3\alpha\beta))\\&=(-b)((-b)^2-3c))\\&=-b(b^2-3c)\\&=-b^3+3bc\end{aligned}[/tex]
The product of the roots α³ and β³ in terms of c is:
[tex]\alpha \cdot \beta = c[/tex]
[tex](\alpha \cdot \beta)^3 = c^3[/tex]
[tex]\alpha^3 \cdot \beta^3=c^3[/tex]
For a quadratic equation in the form x² + bx + c = 0:
The sum of the roots is equal to -b.The product of the roots is equal to c.So for x² + bx + c = 0 with roots α³ and β³:
[tex]x^2-(\alpha^3 + \beta^3)x+(\alpha^3 \cdot \beta^3)=0[/tex]
[tex]x^2-\left(-b^3-3bc\right)x+c^3=0[/tex]
[tex]x^2+\left(b^3-3bc\right)x+c^3=0[/tex]
Therefore, the equation with the roots α³ and β³ is:
[tex]\boxed{x^2+\left(b^3-3bc\right)x+c^3=0}[/tex]
Substitute the given value of c = 2:
[tex]x^2+\left(b^3-3b(2)\right)x+2^3=0[/tex]
[tex]x^2+\left(b^3-6b\right)x+8=0[/tex]
If b³ - 6b + 9 = 0, then (b³ - 6b) = -9.
Substitute this into the equation:
[tex]x^2-9x+8=0[/tex]
Factor:
[tex](x-1)(x-8)=0[/tex]
Therefore, the roots of the equation with the roots α³ and β³ are 1 and 8, so the values of α and β are:
[tex]\alpha^3 =1 \implies \alpha = 1[/tex]
[tex]\beta^3=8 \implies \beta=2[/tex]
To find the real roots of b³ - 6b + 9 = 0, substitute the found values of α and β into the expression for b:
[tex]b=-(\alpha + \beta)[/tex]
[tex]b=-(1+2)[/tex]
[tex]b=-3[/tex]
Therefore, the real root of b³ - 6b + 9 = 0 is b = -3.
We can confirm this by substituting b = -3 into the equation:
[tex]\begin{aligned}(-3)^3-6(-3)+9&=-27+18+9\\&=-9+9\\&=0\end{aligned}[/tex]
As part of an annual review of its accounts, a discount brokerage selects a random sample of 30 customers. Their accounts are reviewed for total account valuation, which showed a mean of $36,900, with a sample standard deviation of $8,250. (Use tDistribution Table.)
What is a 98% confidence interval for the mean account valuation of the population of customers? (Round your answers to the nearest dollar amount.)
Answer:
The sample size is 30.
The sample mean is $36,900.
The sample standard deviation is $8,250.
The confidence level is 98%.
The critical value for a 98% confidence interval with 29 degrees of freedom is 2.457.
The confidence interval is calculated as follows:
(Sample mean - t-critical value * sample standard deviation / sqrt(sample size), Sample mean + t-critical value * sample standard deviation / sqrt(sample size))
(36,900 - 2.457 * 8,250 / sqrt(30), 36,900 + 2.457 * 8,250 / sqrt(30))
(21,668.25, 52,131.75)
Therefore, a 98% confidence interval for the mean account valuation of the population of customers is $21,668.25 to $52,131.75.
Step-by-step explanation:
consider two large independent samples from two populations. the difference in the two sample means has which kind of distribution?
When we have two large independent samples from two populations, the difference in the two sample means will follow an approximate normal distribution.
This is due to the central limit theorem, which states that when we have a large enough sample size (typically, greater than 30), the distribution of the sample means will be normal regardless of the underlying distribution of the populations. As the two samples are independent, the difference in means will also be independent. Therefore, we can use the normal distribution to estimate the probability of observing a certain difference in means. It is important to note that this approximation may not hold for small sample sizes, and the underlying distributions of the populations can also impact the shape of the distribution. We can say that the normal distribution approximation is widely used in statistics and hypothesis testing, making it an essential concept for understanding and interpreting data.
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how many different 7 card hands can be chosen from a standard 52 card deck
Using the combination formula, we calculate that there are 133,784,560 different 7-card hands that can be chosen from a standard 52-card deck.
A standard 52-card deck has 52 unique cards, and to find the number of different 7-card hands that can be chosen, we use the combination formula, which is C(52,7). This formula represents the number of ways to choose 7 cards out of a total of 52 cards, where order does not matter.
The formula for C(52,7) is derived by using factorials. For example, 52! represents 52 x 51 x 50 x 49 x 48 x 47 x 46 x ... x 2 x 1, which is the total number of ways to arrange all 52 cards. The denominator, 7! x 45!, represents the number of ways to arrange the 7 chosen cards out of 52, and also the number of ways to arrange the remaining 45 cards that were not chosen.
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Which of the following are more precise than a weight of 180 pounds? Check
all that apply.
A. 175 pounds
B. 200 pounds
C. 170 pounds
D. 180.4 pounds
Answer:
the answer would be b and d
Step-by-step explanation:
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Aaron withdraws $120 per month
from his savings account. His
account started with $6000.
Just type the number:
f (8 months) =
f (22 months) =
f (4 years) =
Khan
Type yes or no: the input is savings
dollars
dollars
dollars
Type yes or no: in one year the account will be at $4660
Type yes or no: it will take 50 months for the account to hit $0
Step-by-step explanation:
To find f(8 months), we can use the formula:
f(n) = 6000 - 120n
Substituting n = 8, we get:
f(8) = 6000 - 120(8) = 5160
Therefore, f(8 months) is 5160.
To find f(22 months), we can again use the formula:
f(22) = 6000 - 120(22) = 3480
Therefore, f(22 months) is 3480.
To find f(4 years), we need to convert 4 years to months and then use the formula:
f(4 years) = f(48) = 6000 - 120(48) = 48
Therefore, f(4 years) is 48.
Answer to Khan's questions:
- Is the input in savings dollars? Yes, the initial account balance is given in dollars.
- Will the account be at $4660 in one year? No, we cannot determine this without additional information about the interest rate or other factors that may affect the account balance.
- Will it take 50 months for the account to hit $0? No, we cannot determine this without additional information about the interest rate or other factors that may affect the account balance.
A
DX 105°
What is the
measure of angle D?
m/D [?]
Enter the number
of degrees.
Desired graph is attached below.
Steps to draw a desired angle are:
Draw angle ABC of measure 105 degrees.Take a point D in its interior and join BD.Measure angle ABD and angle DBC using a protractor.Add the measures of angle ABD and angle DBC together.Verify that the sum of angle ABD and angle DBC is equal to the measure of angle ABC (which is given as 105 degrees).If the sum of angle ABD and angle DBC is equal to 105 degrees, then the statement is verified.
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Complete question:
Draw an angle ABC of measure 105 degree.take a point D in its interior. Join BD. Verify by measuring that angle ABD +angle DBC=angle ABC.
The box plots below show the distributions of the
numbers of visitors each day to two attractions.
a) Work out the interquartile range of the numbers of
visitors to
i) the museum.
ii) the farm.
b) Copy and complete the sentences below.
Museum
H
Farm
H
0 100 200 300 400 500 600 700 800
Number of visitors
The interquartile range for the museum is greater / less than the interquartile range for the farm.
This suggests that the numbers of visitors to the museum are more/less consistent.
The interquartile range for the museum is 280
The interquartile range for the farm is 200
The interquartile range for the museum is greater than the interquartile range for the farm.
This suggests that the numbers of visitors to the museum are less consistent.
How to find the interquartile rangeThe interquartile range is solved using the formula
= top quartile - bottom quartile
Where
the bottom quartile is at the box's edge, the top side.
the top quartile is towards the box's edge the downside.
the museum
The interquartile range is
= top quartile - bottom quartile
= 500 - 220
= 280
the farm
The interquartile range is
= top quartile - bottom quartile
= 460 - 260
= 200
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Here are the ingredients for making pineapple sorbet for 6 people. 800 g pineapple 4 egg whites ½ lemon
Dan makes pineapple sorbet. He uses 2½ lemons. Work out how many people he makes pineapple sorbet for.
We know that the original recipe is for 6 people, and it requires 800g of pineapple, 4 egg whites, and 1/2 lemon.
If Dan uses 2 1/2 lemons instead of 1/2 lemon, that means he's using 5 times as much lemon juice. Therefore, he's likely making 5 times the original recipe.
So, for Dan's pineapple sorbet, he would need:
800g x 5 = 4000g (or 4kg) of pineapple
4 x 5 = 20 egg whites
1/2 lemon x 2.5 = 1 1/4 lemons (but since we can't really use a quarter of a lemon, we'll just say he needs 1.5 lemons)
Therefore, Dan is making pineapple sorbet for 6 x 5 = 30 people.
WILL GIVE BRAINLIST TO BEST ANSWER
Find the value of x that makes lines u and v parallel
Answer:
x = 8
Step-by-step explanation:
If those two given angles equal each other, then u and v are parallel.
7x - 6 = 5x + 10
2x = 16
x = 8
If x = 8, then lines u and v are parallel.
QUESTION 4 4.1 Tangent BC touches the circle ABDE at B. Chords AD and BE intersect at F. Chord ED is produced to C. AB || EC. It is further given that B₁ = x and A₁ = y 4.1.1 determine the size of c in terms of x and y. 4.1.2Becky says that BCDF is not a cyclic quadrilateral while Teboho insists that it is. Who is correct? Show all you're working in determining your answer.
Becky is correct if x + y = 180° , indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x + y ≠ 180°.
What is a Cyclic Quadrilatera l?A cyclic quadrilateral, also known as an inscribed quadrilateral in Euclidean geometry, is a quadrilateral with all of its vertices on a single circle.
To determine the size of angle C in terms of x and y, we can use the fact that tangent BC touches the circle ABDE at B.
This means that angle C is equal to the angle formed between the chord AD and the tangent BC at point B.
4.1.1
Since AB || EC, we can use the alternate interior angles theorem to determine the relationship between angles C and A₁.
Angle C is equal to angle A₁ because they are corresponding angles.
Therefore, the size of angle C is y.
4.1.2 - To determine if BCDF is a cyclic quadrilateral
In order to check if BCDF is cyclic, we need to determine if the opposite angles in the quadrilateral add up to 180° .
Let's consider angle BCD and angle BFD:
Angle BCD is equal to angle B₁ (given) and is represented by x.
Angle BFD is equal to angle A₁ (since BCDF is a cyclic quadrilateral) and is represented by y.
If x + y = 180 degrees, then BCDF is a cyclic quadrilateral.
conclusively , Becky is correct if x + y = 180°, indicating that BCDF is a cyclic quadrilateral. Teboho's claim would be valid if x + y ≠ 180°.
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The expression 54a + 42c represents the cost for a adults and c children to attend a play. What is the cost for 2 adults and 3 children to attend?
O A. $102
O B. $300
O C. $234
O D. $480
Answer:
Step-by-step explanation:
Please help me this is for my math assignment and I don't understand it.
The simplified expression in this problem has the result given as follows:
40.
How to simplify the expression?The expression for this problem is defined as follows:
[tex]\frac{(8^4)^3 \times 5^2 \times 5^3}{8^7 \times (8 \times 5)^4}[/tex]
Applying the power of power rule, which states that we keep the bases and multiply the exponents we, have that:
[tex](8^4)^3 = 8^{12}[/tex][tex](8 \times 5)^4 = 8^4 \times 5^4[/tex]Hence:
[tex]\frac{8^{12} \times 5^2 \times 5^3}{8^7 \times 8^4 \times 5^4}[/tex]
When two terms with the same base and different exponents are multiplied, we keep the bases and add the exponents, hence:
[tex]\frac{8^{12} \times 5^5}{8^{11} \times 5^4}[/tex]
When two terms with the same base and different exponents are divided, we keep the bases and add the exponents, hence:
8 x 5 = 40.
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35 > 4x, if x = 7 ? What would the equation be then?
35>28
For this problem, just replace x with seven and multiply by four.
35 > 4•7
This should get us to our new equation, 35 > 28
a city with more than 100,000 residents located within a metropolitan area but that is not the central city and that has maintained a double-digit growth rate in recent years is known as a
a city with more than 100,000 residents located within a metropolitan area but that is not the central city and that has maintained a double-digit growth rate in recent years is known as an "edge city."
A suburban city refers to a city with more than 100,000 residents located within a metropolitan area but that is not the central city. These cities are often characterized by their proximity to a larger city, and they may offer a more suburban or residential feel compared to the central city. Additionally, suburban cities have maintained a double-digit growth rate in recent years due to factors such as increased economic opportunities and a higher quality of life.
Edge cities are urban areas that have emerged on the periphery of major metropolitan areas, often near major highways or other transportation hubs. These cities experience significant growth due to their strategic location, and they attract businesses, retail centers, and housing developments. This leads to a continuous increase in population and rapid expansion, which can result in a double-digit growth rate.
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jaffar bought 5 books. the prices of 4 of the books are $15, $16, $17, and $19. the average he paid for the 5 books is $17. how much did he pay for the fifth book?
Answer:
$18-----------------------
The average price Jaffar paid for the 5 books is $17.
To find the total cost of the 5 books, we multiply the average price by the number of books:
$17 * 5 = $85Now, we'll add up the prices of the first four books:
$15 + $16 + $17 + $19 = $67Finally, we'll subtract the sum of the first four books from the total cost to find the price of the fifth book:
$85 - $67 = $18So, Jaffar paid $18 for the fifth book.
Patrick scored 70, 74, 72, 71, 73, and 96 on six science tests. Which measure of central tendency best describes Patrick's scores?
The best measure of central tendency for Patrick's scores would be the median, which is 72.5.
To determine which measure of central tendency best describes Patrick's scores, let's consider the three main measures: mean, median, and mode.
1. Mean: Calculate the average by adding all scores and dividing by the number of tests.
(70 + 74 + 72 + 71 + 73 + 96) / 6 = 456 / 6 = 76
2. Median: Arrange the scores in ascending order and find the middle value.
70, 71, 72, 73, 74, 96
There are two middle values (72 and 73), so the median is their average: (72 + 73) / 2 = 72.5
3. Mode: Identify the most frequent score.
There is no mode, as all scores occur only once, except for the outlier (96).
The best measure of central tendency for Patrick's scores would be the median, which is 72.5. The median is less influenced by the outlier (96) and provides a more accurate representation of Patrick's typical performance on the science tests.
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5 6 si 7 urgent va rog
Please determine whether they are true or false if all questions answered and are correct will give brainlessly
True
False
True
1. True, the legs of a right triangle are connected to the right angle.
2. False, the hypotenuse of a right triangle is a specific side that is opposite to the right angle, and it is always the longest side of the triangle. The other two sides are called legs.
3. True, the side opposite to the right angle in a right triangle is called the hypotenuse.
Given the circle below with secants NOP and RQP. If QP = 9, RQ = 21 and
OP 10, find the length of NO. Round to the nearest tenth if necessary.
The length of the segment NO is 17.9
The given parameters are;
Length of side, QP = 9
Length of QO = 14
The length of segment NO we have to find.
NO² = qo×(qp×qo)
Plug in the values of qo, qp
Which gives NO² =14(9×14)
=322
NO=17.9
Hence, the length of the segment NO is 17.9
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Given the circle below with tangent \overline{NO} NO and secant \overline{QPO} QPO . If QP=9 and QO=14, find the length of \overline{NO} NO . Round to the nearest tenth if necessary. Q
how many solutions does 5x-5=4(x+5) have? pleaseeeeeeeeeeeeeeeeeeee
In the context of chi square, which pattern of cell frequencies in a 2x2 table would indicate that the variables are independent? a. Only the cells in the top row of the table have cases in them b. There are no cases in any celf c. There are a different number of cases in each of the tour cells d. All cell trequencics are exactly the same
Therefore, in a 2x2 table, the pattern of cell frequencies that would indicate independence is d. All cell frequencies are exactly the same.
In a 2x2 contingency table, the expected cell frequencies under the null hypothesis of independence are equal for all cells. If the observed cell frequencies in the table are approximately equal to the expected cell frequencies, then we can conclude that there is no significant association between the two variables being studied. In other words, the pattern of observed cell frequencies is consistent with the null hypothesis of independence. Therefore, if all cell frequencies are exactly the same, it suggests that the variables are independent, as each cell has an equal chance of being filled by any observation regardless of the value of the other variable.
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