Answer:
its 4xy and 12x
( options B and C)
hope that helped :)
Answer:
its 4xy and 12x
Step-by-step explanation:
which one of these numbers is not like the others?
21,15,6,16,27
Answer:
16
Step-by-step explanation:
It's hard to tell what the what the problem means by "not like the others", but here's a guess.
16 is a perfect square. 16 = 4^2
None of the other numbers are perfect squares.
Also, 16 is not divisible by 3. All other numbers are divisible by 3.
Which statement illustrates the distributive property?
3(4+5)= 3(4)+5
3(4+5)= 3(4)+3(5)
3[(4)+(5)] = 3(4)+3(5)
3[(4)(5)] = [3(4) ][ 3(5)]
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
Answer:
3(4+5)= 3(4)+3(5)
Step-by-step explanation:
There were 30 voters. Exactly 10% of voters chose which candidate?
Candidate A-12
Candidate B-3
Candidate C-6
Candidate D-9
Answer:
CANDIDATE B
Step-by-step explanation:
U
Proving the Parallelogram Diagonal Theorem
Given: ABCD is a parallelogram.
Diagonals AC, BD intersect at E.
Prove: AE CE and BE DE
Statements
✓ 1. ABCD is a parallelogram
Reasons
1. given
Correctl Assemble the next
statement.
) Intro
From the given parameters with reasons and statements, we have proven that AE = CE and BE = DE from; Properties of Parallelogram and ASA Congruence Postulate.
How to do a two - column proof?Statement 1; ABCD is a parallelogram
Reasons 1; given
Statement 2; ∠ABE and ∠CDE are alternate Interior angles
Reason 2; Definition of Alternate Interior angles
Statement 3; ∠BAE and ∠DCE are alternate Interior angles
Reason 3; Definition of Alternate Interior angles
Statement 4; AB = CD
Reason 4; Parallelogram side theorem
We want to prove that AE = CE and BE = DE
From properties of parallelogram, we can say that ∠CBD = ∠ABD and also ∠BCA = ∠DAC
Thus, it means that; ΔBEC ≅ ΔAED
Thus, from ASA Congruency postulate, we can say that;
AE ≅ CE and BE ≅ ED
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Every 8 days the cafeteria sells pizza and every 10 days they sell banana pudding. Today they had both, how many days till they sell both again?
Answer:
40 days
Step-by-step explanation:
The next that the two lineup is forty days.
8,16,24,32,40
10,20,30,40
40 is when they meet up
Mr.Gonzales is replacing a cylindrical air-conditioning duct. He estimates the radius of the duct by folding a ruler to form two 6-in. tangents to the duct. The tangents form an angle. Mr. Gonzales measures the angle bisector from the vertex to the duct. It is about 2.75 inches long. What is the radius of the duct.
Answer:
The radius of the duct is [tex]5\frac{15}{88}\ in[/tex] or [tex]5.17\ in[/tex]
Step-by-step explanation:
we know that
At the point of tangency, the tangent to a circle and the radius are perpendicular lines
so
In the right triangle formed
Applying the Pythagorean Theorem
[tex](r+2.75)^2=r^2+6^2[/tex]
Remember that
[tex]2.75\ in=2\frac{3}{4}=\frac{11}{4}\ in[/tex]
substitute
[tex](r+\frac{11}{4})^2=r^2+6^2[/tex]
solve for r
[tex]r^2+\frac{11}{2}r+\frac{121}{16}=r^2+36\\\frac{11}{2}r=36-\frac{121}{16}[/tex]
Multiply by 16 both sides
[tex]88r=576-121\\88r=455\\r=\frac{455}{88}\ in[/tex]
convert to mixed number
[tex]r=\frac{455}{88}\ in=\frac{440}{88}+\frac{15}{88}=5\frac{15}{88}\ in[/tex] ----> exact value
The approximate value is [tex]5.17\ in[/tex]
What is the range of this relation?
(5,-11)
(5,13)
(-7,8)
Answer:
{-11,8,13}
Step-by-step explanation:
The domain is the input values (or x)
The range is the output values (or y)
The range is (-11,8,13)
1 point
The figure is made up of 4
overlapping rectangles, each of
which are 8 cm by 4 cm. All lines
meet at right angles. What is the
area of the figure? *
8 cm
4 cm
Answer:
128cm
Step-by-step explanation:
since there are 4 triangles that have an area of 8*4 each, you can multiply 8*4 together to get 32. Then you would multiply 32 by 4 to get the entire area of the whole figure.
Using 3.14 as an approximation for pi, find the diameter, circumference, and area of the circle with a radius of 5 cm. Do NOT include units in your answer. Part A Diameter Part B Centimeter Part C Area
The diameter of this circle is 10, the circumference is 31.4 and the area is 58.5.
Because the diameter of a circle is twice its radius, we have:
d = 2*r
d = 2*5 = 10
The following formula calculates the circumference of a circle:
2*pi*r = circumference
2*3.14*5 circumference
10 times 3.14 equals 31.4
The following formula calculates the area of a circle:
area = pi*r²
area = 3.14*(5)²
area = 3.14*25
area = 78.5
This circle has a diameter of 10, a circumference of 31.4, and an area of 58.5.
Complete question:
Find the diameter, circumference, and area of the circle with a radius of 5 cm.
Bed & Bath, a retailing company, has two departments—Hardware and Linens. The company's most recent monthly contribution format income statement follows: Department Total Hardware Linens Sales $ 4,190,000 $ 3,110,000 $ 1,080,000 Variable expenses 1,264,000 858,000 406,000 Contribution margin 2,926,000 2,252,000 674,000 Fixed expenses 2,290,000 1,480,000 810,000 Net operating income (loss) $ 636,000 $ 772,000 $ (136,000 ) A study indicates that $373,000 of the fixed expenses being charged to Linens are sunk costs or allocated costs that will continue even if the Linens Department is dropped. In addition, the elimination of the Linens Department will result in a 15% decrease in the sales of the Hardware Department.
Answer:
By eliminating Linens department net operating income fell by $574,800.00
Step-by-step explanation:
The question requires that the monthly contribution income statement be prepared when the Linens is closed or eliminated,incorporating the unavoidable fixed costs of $373,000 as well as the fall in sales of Hardware by 15%.
Monthly Contribution Income Statement:
Sales($3,110,000)*(1-15%) $2,643,500.00
Variable expenses($858,000)*(1-15%) ($729,300.00)
Contribution margin $1,914,200.00
Fixed expenses($1,480,000+$373,000) ($1,853,000.00)
Net operating income $61,200.00
Reduction in net operating=$636,000-$61,200.00=$574,800
Alternatively:
Lost contribution from closing Linens department $674,000.00
Lost contribution from Hardware(15%*$2,252,000) $ 337,800.00
Total lost contribution $1,011,800.00
Less avoidable fixed costs($810,000-$373,000) ($437,000.00)
Reduction in profits company-wide $574,800.00
The sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
Sunk Costs and Allocated Costs:
- $373,000 of the fixed expenses allocated to the Linens Department are sunk costs or allocated costs. These costs will continue even if the Linens Department is dropped. They should not be considered in the decision-making process as they will not change with the elimination of the department.
2. Impact on Hardware Department:
- Dropping the Linens Department will result in a 15% decrease in the sales of the Hardware Department. This means that the sales of the Hardware Department will decrease by $1,110,000 (15% of $3,110,000, Linens sales). This decrease in sales will impact the contribution margin of the Hardware Department.
3. Contribution Margin Calculation:
- The contribution margin of the Hardware Department before dropping Linens is $2,252,000. With a 15% decrease in sales, the new contribution margin for the Hardware Department is $1,142,000.
4. Net Operating Income:
- The net operating income of the Hardware Department after dropping the Linens Department is calculated by subtracting the fixed expenses of the Hardware Department and the revised contribution margin from the total sales.
5. Overall Impact:
- Dropping the Linens Department will result in a positive impact on the overall net operating income of Bed & Bath. The increased net operating income from the Hardware Department ($772,000) will offset the loss from dropping the Linens Department ($136,000).
Considering the sunk costs, allocated costs, and the impact on the Hardware Department's sales and profitability, dropping the Linens Department appears to be a financially prudent decision for Bed & Bath.
What is the value of d
Answer:71.5
Step-by-step explanation:
2d+37+1+38=2d+76=180
180-76=2d+143
143divided by 2 =71.5
Answer:
d = 57 degrees.
Step-by-step explanation:
The 3 angles in a triangle add up to 180 degrees, so:
2d + 1 + 38 + 27 = 180
2d = 180 - (1 + 38 + 27)
2d = 180 - 66 = 114
d = 114/2
d = 57 degrees.
Find the value of x to the nearest tenth.
Please help it’s due today! Will give brainliest! 15 points! :)
Answer:
The answer to your question is x = 14.7
Step-by-step explanation:
Data
∠A = 20°
∠B = 46
a = 7
b = x
Process
To solve this problem use, the law of sines. This law states that the ratio of a side of a triangle to the sine of the opposite angle is the same for all three sides.
The law of sines for this problem is
x / sin 46 = 7 / sin 20
-Solve for x
x = 7 sin 46 / sin 20
-Simplification
x = 7 (0.719) / 0.342
x = 5.035/0.342
-Result
x = 14.7
What is the probability that you turn to page 45?
Type your answer in the format:
3/4
with no spaces.
Answer:
1/60
Step-by-step explanation:
Solve the equation
45÷x=3/4
Brainliest would be appreciated
Find the perimeter of the polygon.
W: 4ft
L: 7ft
How do I slove it?
If your looking to solve the perimeter, your looking for the total distance around the box. Add up the length of each of the 4 sides. The formula would be: (w x 2)+(Lx2)
(4x2)+(7x2)=
8+14=
22
perimeter is "22"
what is the are of a rectangle with the height of 2x^4 and a width of x^2+8x+15?
Answer:
the length is x+5
Step-by-step explanation:
1.(x^2+8x+15)/(x+3)
2.(x+5)(x+3)(x+3)X=5
Answer:
2x^6 + 16x^5 + 30x^4
Step-by-step explanation:
You just need to multiply the two together; it's the same as any rectangle.
What is the value of s?
Answer:
The answer to your question is 33°
Step-by-step explanation:
Data
∠1 = 39°
∠2 = 108°
∠3 = ?
Process
To solve this problem, remember that the sum of the internal angles in a triangle equals 180°.
Then,
∠1 + ∠2 + ∠3 = 180°
-Substitution
39° + 108° + ∠3 = 180°
-Solve for ∠3
∠3 = 180 - 39 - 108
-Simplification
∠3 = 180° - 147°
-Result
∠3 = 33°The time needed to paint a fence varies directly with the length of the fence and inversely with the number of painters. If it takes seven hours to paint 280 feet of fence with two painters, how long will it take four painters to paint 720 feet of fence?
Answer:
It will take 9 hours with 4 painters to paint 720 feet of fence.
Step-by-step explanation:
Given that,
The time needed to paint a fence varies directly with the length of the fence
[tex]t\propto l[/tex] .......(1)
and inversely with the number of painters
[tex]t\propto \frac1P[/tex].....(2)
Combination of (1) and (2) is
[tex]t\propto \frac lP[/tex]
where t represents time, [tex]l[/tex] represents length of fence, P represents number of painters.
Again we can write the above equation as
[tex]\frac{t_1}{t_2}=\frac{\frac{l_1}{l_2}}{\frac{P_1}{P_2}}[/tex]
[tex]\frac{t_1}{t_2}=\frac{l_1P_2}{l_2P_1}[/tex]
Given that,
It takes 7 hours with 2 painters to paint 280 feet of fence .
We need to find time to paint 720 feet of fence with 4 painters.
[tex]t_1[/tex]=7 hours, [tex]l_1[/tex]=280 feet, [tex]P_1[/tex]=2,
[tex]t_2[/tex]=? , [tex]l_2[/tex] = 720 feet, [tex]P_2[/tex]=4
[tex]\therefore \frac{7}{t_2}=\frac{280\times 4}{720\times 2}[/tex]
[tex]\Rightarrow \frac{t_2}{7}=\frac{720\times 2}{280\times 4}[/tex]
[tex]\Rightarrow {t_2}}=\frac{720\times 2\times 7}{280\times 4}[/tex]
[tex]\Rightarrow t_2=9[/tex]
It will take 9 hours to paint 720 feet of fence with 4 painters.
The time it takes for four painters to paint a 720 feet fence is calculated using direct and inverse variation, resulting in 9 hours, using the constant of variation determined from the initial condition provided by the student.
Explanation:Direct and Inverse Variation in Painting Jobs
The student's question involves direct and inverse variation, which means we need to solve for the time based on the length of the fence and the number of painters. Initially, it takes seven hours for two painters to paint 280 feet of fence. This scenario sets up our proportion. When the length of the fence and the number of painters changes, the time to paint the fence will also change according to the direct and inverse relationships.
To find the time it takes for four painters to paint 720 feet of fence we use the formula [tex]T = (k \times L) / P[/tex], where T is the time needed, L is the length of the fence, P is the number of painters, and k is a constant of variation. Using the initial condition, we can solve for k by rearranging the formula to [tex]k = (T \times P) / L[/tex]. Substituting the initial condition values, we find that [tex]k = (7 hours \times2 painters) / 280 feet[/tex], which simplifies to k = 1/20.
To find the time it will take for four painters to paint 720 feet, we use the formula with our calculated constant of variation and the new conditions: T = (1/20 × 720 feet) / 4 painters, which gives us T = 9 hours. Therefore, it will take four painters 9 hours to paint 720 feet of fence.
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I need help asap :):):)
Answer: m + 4
Step-by-step explanation:
Expressions don't have equal signs and the values are separated by a symbol/s.
Answer:
m+4
An expression is the problem.
Ex: 2+3=5 2+3 Would be the expression here
The number of bacteria grown in a lab can be modeled by p(t)=300(2)^4t ,where t is the number of hours. Which expression is equivalent to ?
1) 300 (8)^t
2) 300 (16)^t
3) 300^t (4)^t
4) 300^2t (2)^2t
Answer:
2. 300(16)∧t
Step-by-step explanation:
p(t) = 300(2)∧4t
where b is the number of hours
2∧4t =2∧4(t) 2 x2 x2 x2 = 16∧t
p(t) = 300(2)∧4t = 300(16)∧t
The points scored by a basketball team in its last 5 games are shown. The mean amount of points is 83.2. The median is 72 points. Which measure of center best describes the data? Show work or explain.(5pts.)5.Armand is training for a video game competition. He wants to practice an average of 40 minutes a day. His training log for the week is below. A.How many minutes does he need to practice on Sunday to meet his goal? Show work.(10pts.)6.Show work:(5 pts.)Points Scored73707271130Monday53Tuesday24Wednesday35Thursday60Friday20Saturday65Sunday
Answer:
1. The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance
2. This implies that Armand needs to train for 23 minutes on Sunday
Step-by-step explanation:
The mean (also called arithmetic mean) is the central value of a given set of data; gotten by dividing the sum of the values in the data set by the number of items in the data set.
Mathematically,
Mean (m) = ∑ [tex]\frac{x_i}{n}[/tex]
where [tex]x_{i}[/tex] = the sample
n = the number of items in the sample
The median is the central value in a distribution or given set of data after the data has been arranged sequentially either in ascending or descending degree. In simpler terms, it is regarded as the 'middle number'. The basic advantage of the median over the mean is that unlike the mean which can be skewed by outliers (extremely high or low values) in a data set, the median stays close to presenting a true value
1.
Data for the basketball team in its last 5 games = 73, 70, 72, 71, 130
Mean (m) = (73 + 70 + 72 + 71 + 130) ÷ 5
Mean (m) = 416 ÷ 5 = 83.2
Arranging the data sequentqially, we have: 70, 71, 72, 73, 130
Median ([tex]{\displaystyle a}[/tex]) = 72
The median is a much more precise measure of the team's perfomance & it showcases the true picture of the team's average performance. The mean was skewed by the result of the team's last game where the team scored 130 points (an outlier)
2.
Armand's training data (the week begins on Monday & ends on Sunday):
Monday = 53 minutes, Tuesday = 24 minutes, Wednesday = 35 minutes,
Thursday = 60 minutes, Friday = 20 minutes, Saturday = 65 minutes,
Sunday = ?
Since Armand intends to practise an average of 40 minutes for the week (7 days), we calculate thus
Mean (m) = sum of time Armand spends training ÷ number of days Armand spends training
Target Mean = 40 minutes, sum of time = 53 + 24 + 35 + 60 + 20 + 65 + x = 257 + x
where x = minutes Armand needs to practice on Sunday to meet his goal
number of days = 7
40 = (257 + x) ÷ 7
Make x the subject of the formula, we have:
257 + x = 40 * 7
x = 280 - 257 = 23
x = 23 minutes
This implies that Armand needs to train for 23 minutes on Sunday if he is to make his targeted weekly average of 40 minutes
Fernando is making 30 sundaes with mint, chocolate,and vanilla ice cream.1/3 of the Sunday's are mint ice-cream and 1/2 of the remaining sundaes are chocolate. The rest are chocolate.The rest are vanilla.How many sundaes will be vanilla ?
Answer:
10 sundaes will be vanilla.
Step-by-step explanation:
Given:
Fernando is making 30 sundaes with mint, chocolate,and vanilla ice cream.
1/3 of the Sunday's are mint ice-cream.
And 1/2 of the remaining sundaes are chocolate.
The rest are vanilla.
Now, to find the number of sundaes that will be vanilla.
Fernando is making sundaes total = 30.
So, the quantity of sundaes that are mint ice-cream:
[tex]\frac{1}{3} \ of\ 30\\\\=\frac{1}{3} \times 30\\\\=10.[/tex]
Thus, 10 sundaes are mint ice-cream.
So, the remaining sundaes are:
[tex]30-10=20.[/tex]
Thus, the remaining sundaes are = 20.
Now, to get the quantity of chocolate sundaes of the remaining sundaes:
[tex]\frac{1}{2} \ of\ 20\\\\=\frac{1}{2} \times 20\\\\=10.[/tex]
Hence, 10 sundaes are chocolate of the remaining 20 sundaes.
As, given the rest are vanilla.
Now, to get the vanilla sundaes we subtract the 10 chocolate ice-cream from the 20 remaining sundaes:
[tex]20-10=10.[/tex]
Therefore, 10 sundaes will be vanilla.
I need help asap :):):)
Step-by-step explanation:
Cost of 10 miles = 0.25 × 10 = 2.5
When we add 5 = 2.5 + 5 = 7.5
Option A is the correct answer
Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of ±2 percent with 90 percent confidence. What is the necessary sample size?
Answer:
Hence, the minimum required sample size (n) should be = 1692
Step-by-step explanation:
Solution:-
- The estimation error, E = 2%
- The confidence level, CI = 90 %
- Since the proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy are unknown we will assume the corresponding proportion to be p = 0.58
- The required sample size is a function of confidence value and error of estimation (E):
[tex]n = p*( 1 - p ) * (\frac{Z-critical}{E})^2[/tex]
Where,
- The critical value of the confidence level = 90% would be:
significance level ( α ) = 1 - CI = 1 - 0.90 = 0.1
Z-critical = Z_α/2 = Z_0.05 = 1.645
- The required sample size (n) can be calculated:
[tex]n = 0.5*( 1 - 0.5 ) * (\frac{1.645}{0.02})^2\\\\n = 1691.265[/tex]
- Hence, the minimum required sample size (n) should be = 1692
Jake, Elijah, and Zaire had 65 Pokemon cards. Jake had two more cards than Elijah, and Elijah had three more cards than Zaire. How many cards did Jake have?
Answer: Jake has 24 cards
Step-by-step explanation:
Let x represent the number of Pokemon cards that Elijah has.
Jake had two more cards than Elijah. It means that the number of cards that Jake has is x + 2
Elijah had three more cards than Zaire. It means that the number of cards that Zaire has is x - 3
Jake, Elijah, and Zaire had 65 Pokemon cards. It means that
x + x + 2 + x - 3 = 65
3x - 1 = 65
3x = 65 + 1 = 66
x = 66/3 = 22
The number of cards that Jake has is
x + 2 = 22 + 2 = 24
Answer:
24
Step-by-step explanation:
Given:
Total number of cards, T = 65
Let's take number of Elijah's cards as E
Jake's cards = J
Zaires's cards= Z
So we have,
J+E+Z = 65
We are told Jake had 2 more than Elijah=
J= E+2
Elijah had 3 more than Zaire. number of Zaire's card will be=
Z= E-3
We now have:
E+2+E-3+E = 65
3E = 65+1
3E = 66
E = 66/3
E=22
Number of Elijah's card is 22
We are told Jake had 2 more cards than Elijah. Therefore number of Jake's cards will be=
E + 2
= 22 + 2 = 24
Number of Jake's cards = 24
A decision model that presumes an environment where problems are clearly defined, all possible action alternatives are known, and the consequences of the alternatives are clear is known as a ________ decision model.
a. behavioral.
b. classical.
c. optimizing.
d. satisficing.
Answer:
B. Classical
Step-by-step explanation:
By definition, classic decision model is where the problems are clearly defined, all possible actions and alternatives are known, and the consequences of the alternatives are clear.
A sample is selected from a population with μ = 46, and a treatment is administered to the sample. After treatment, the sample mean is μ = 48 with a sample variance of σ² = 16. Based on this information, what is the value of Cohen’s d?
Answer:
0.5
Step-by-step explanation:
Solution:-
- The sample mean before treatment, μ1 = 46
- The sample mean after treatment, μ2 = 48
- The sample standard deviation σ = √16 = 4
- For the independent samples T-test, Cohen's d is determined by calculating the mean difference between your two groups, and then dividing the result by the pooled standard deviation.
Cohen's d = [tex]\frac{u2 - u1}{sd_p_o_o_l_e_d}[/tex]
- Where, the pooled standard deviation (sd_pooled) is calculated using the formula:
[tex]sd_p_o_o_l_e_d =\sqrt{\frac{SD_1^2 +SD_2^2}{2} }[/tex]
- Assuming that population standard deviation and sample standard deviation are same:
SD_1 = SD_2 = σ = 4
- Then,
[tex]sd_p_o_o_l_e_d =\sqrt{\frac{4^2 +4^2}{2} } = 4[/tex]
- The cohen's d can now be evaliated:
Cohen's d = [tex]\frac{48 - 46}{4} = 0.5[/tex]
Final answer:
0.5, representing a medium effect size.
Explanation:
To calculate Cohen's d, we use the formula:
d = (M1 - M2) / SD
Where M1 is the mean of the population before treatment, M2 is the mean after treatment, and SD is the standard deviation of the population. Given that M1 = 46, M2 = 48, and the sample variance is σ2 = 16, we first need to find the standard deviation (SD), which is the square root of the variance.
SD = sqrt(σ2) = sqrt(16) = 4
Next, we apply the values to Cohen's d formula:
d = (48 - 46) / 4
d = 2 / 4 = 0.5
This gives us a Cohen's d value of 0.5, which indicates a medium effect size according to Cohen's benchmarks.
3+3
(This is just to get you points or complete challenges)
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = 2.5 x + 3 intersect the circle with radius 4 and center (0, 3)?
Answer:
The point at which the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) is x = 1.49
Step-by-step explanation:
Here we have the equation of a circle = (x - h)² + (y-k)² = r²
Where (h, k) is the coordinate of the center
Therefore, we have
(x - 0)² + (y - 3)² = 4²
Which gives x² + (y - 3)² = 16
Since the line y = 2.5·x + 3 we have
x² + ( (2.5·x + 3 ) - 3)² = 16
x² + (2.5·x)² = 16
x² + 6.25·x² = 16
7.25·x² = 16
x² = 16/7.25 = 2.21
x = 1.49
That is the line y = 2.5·x + 3 intersect with the circle of radius 4 and center (0, 3) at x = 1.49.
The point of intersection in the first quadrant of the given line y = 2.5x + 3 and the given circle x² + (y - 3)² = 16, can be found by substituting the equation of the line into the equation of the circle and then solving for x and y.
Explanation:The subject of this question is the intersection of a line and a circle in the first quadrant of a coordinate plane. The circle is defined by the equation (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius. For a circle with center at the origin (0, 3) and radius 4, the equation is x² + (y - 3)² = 16.
The line is defined by the equation y = 2.5x + 3. To find the intersection point, we substitute this equation into the equation of the circle, resulting in x² + (2.5x)² - 6x + 9 = 16. Solving this quadratic equation gives the x-coordinates of the intersection points. Since we are only interested in the first quadrant, we pick the positive root. Substituting this value of x into y = 2.5x +3 gives the corresponding y-coordinate, defining the point of intersection in the first quadrant.
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Keith's Catering charges a $100 setup fee and $25 per
person served. Zoey's Catering uses the table below to
calculate catering charges.
Number of
People Served
Total Cost
(y)
10
$325
20
$525
30
$725
Which Caterer charges the most per person, and how much more?
Answer:
Keith charges more per person
Step-by-step explanation:
10 = 325
20 = 525
30 = 725
Zoey's price goes up 200 for every 10 people making her setup fee 125 (325-200=125). 200 per 10 people is 20 per person
Who is the snoozer?
Davis: the snoozer was either Rawls or Charlton
Rawls: neither Vongy nor I was asleep
Charlton: both Rawls and Davis are lying
Bobbins: only one of the Rawls or Davis is telling the truth.
Vongy: Bobbins is a liar.
When the board chairperson (she was not questioned) was consulted, she said that three of the board members always tell the truth and two of them always lie. Who slept in the board meeting?
Answer:
Charlton is the snoozer!
Step-by-step explanation:
"If Charlton is telling the truth, that means that both Davis and Rawls are the liars; in particular, Vongy is telling the truth, which would mean that Bobbins is also a liar, contradicting the fact that there are only two liars and there three truth-tellers.
So Charlton is lying. That means that at most one of Davis and Rawls are lying.
If Bobbins is telling the truth, then the second liar must be one of Rawls and Davis, which would again mean that Vongy is telling the truth, making Bobbins a third liar; this is impossible, so Bobbins is lying.
So we now know that the two liars are Charlton and Bobbins, and the remaining three are truth-tellers.
Therefore, the snoozer is either Rawls or Charlton (since Davis is telling the truth), but cannot be Rawls (since Rawls is telling the truth).
So Charlton is the one who fell asleep."