Answer:
3
Step-by-step explanation:
the initial statement is
y ∝ 1 /x
to convert to an equation multiply by k the constant
of variation
y = k × 1 /x = k /x
to find k use the given condition
y = 5 when x = 6
y = k/ x ⇒ k = y x = 5 × 6 = 30
y = 30 /x
when
x = 10
then
y = 30 /10 = 3
Answer: y = 3
Step-by-step explanation:
In inverse variation, as one variable increases, the other variable decreases and as one variable decreases, the other increases.
We would introduce a constant of proportionality, k. Therefore,
y = k/x
When y = 5 , x = 6
Therefore,
5 = k/6
Cross multiplying by 6, it becomes
k = 6 × 5 = 30
The expression becomes
y = 30/x
Therefore, when x is 10,
y = 30/10
y = 3
{(2,4),(3,5),(4,6),(5,8)}
Step-by-step explanation:
The given four sides of quadrilateral = (2, 4), (3, 5), (4, 6) and (5,8)
To find, the area of the quadrilateral = ?
We know that,
The area of quadrilateral [tex]=\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
[tex]=\dfrac{1}{2} [2( 5-6)+3( 6-8)+4( 8-4)+5(4-5)][/tex]
[tex]=\dfrac{1}{2} [2(-1)+3(-2)+4(4)+5(-1)][/tex]
[tex]=\dfrac{1}{2} (-2-6+16-5)[/tex]
[tex]=\dfrac{1}{2} (16-13)[/tex]
= [tex]\dfrac{3}{2}[/tex] units
Thus, the area of the quadrilateral is [tex]\dfrac{3}{2}[/tex] units.
Tommy's heart aches and he needs a minor surgery to mend it. Before you sharpen your scalpel, you have to make sure that you operate on correct organ. Where is Tommy's hear
Answer:
The heart is located in the middle of the 2 lung's in the middle of the chest and slightly to the left side of the chest.
Step-by-step explanation:
The heart is a muscular organ of the size of a fist just behind and to the left of the breastbone. The cardiovascular system is the heart pumping blood across the artery and vein network.Behind your sternum and between your two lungs your heart is found. The heart lies closer to the front of the chest and in the front of the spine. Your diaphragm, stomach and liver are underneath your heart.
Triangle L N M is shown. Angle L N M is 90 degrees, angle N M L is 48 degrees, and angle M L N is 42 degrees. Consider △LMN. m∠L + m∠M = ° sin(L) = sin(M) =
Answer:
m∠L + m∠M = 90° sin(L) = 0.66913sin(M) = 0.74314Step-by-step explanation:
The sum of the two angles is ...
m∠L + m∠M = 42° +48° = 90°
__
A calculator can show you the sines of these angles.
sin(42°) ≈ 0.66913
sin(48°) ≈ 0.74314
_____
The two acute angles of a right triangle always have a sum of 90°.
In triangle LNM, the sum of angles L and M is 90°. The sine values for angles L and M are approximately 0.6691 and 0.7431 respectively.
The sum of the measures of angles L and M can be calculated as follows:
m∠L + m∠M = 42° + 48°
= 90°
For a right triangle, the sine of one acute angle is equal to the cosine of the other acute angle. Therefore, using trigonometry:
sin(L) = sin(42°)
≈ 0.6691
sin(M) = sin(48°)
≈ 0.7431
Thus, the sum of angles L and M is 90°, and the sine values are approximately 0.6691 and 0.7431 respectively.
having trouble with this and 3 other problems
Answer:
a.) 10
b.) -2
c.) 6
d.) y = 6
e.) T = π
f.) y = -6cos(2t) + 4
Step-by-step explanation:
a.) Max value is the highest value in the y-axis. It peaks at y=10
b.) Min value is the lowest value in the y-axis. Peaks at y=-2
c.) Amplitude is how high the peak is from the midpoint. It could be found by taking the average of the peaks. (10 - (-2))/2 = 6
d.) y = 6
e.) T = π
f.) General equation for a sinusoidal wave is
y = Acos(ωt - Ф) + k
y = Acos((2π/T)t - Ф) + k
The graph started at it's min, so the amplitude must had been fliped upsidedown because it normally starts at the max. Therefore I must make my equation negative to flip it.
y = -Acos((2π/T)t - Ф) + k
A = amplitude = 6T = period = πФ = phaseshift = 0k = shift_in_y_direction = 4 , because shifting from -6 to -2 is shifting 4 units upy = -(6)cos((2π/(π))t - (0)) + (4)
y = -6cos(2t) + 4
A vertical pole is supported by a wire that is 26 feet long. If the wire is attached to the ground 24 feet away from the base of the pole, how many feet up the pole should the wire be attached?
The answer is in the attachment
Final answer:
Using the Pythagorean theorem, the calculation shows that the wire should be attached 10 feet up the pole to support it if the wire is 26 feet long and attached to the ground 24 feet away from the base of the pole.
Explanation:
The question asks how high up the pole a wire should be attached if the pole is supported by a wire that is 26 feet long and is attached to the ground 24 feet away from the base of the pole. This scenario forms a right triangle with the ground and the pole as the perpendicular sides, and the wire as the hypotenuse. To solve for the height of the pole where the wire should be attached (the vertical side of the triangle), we can use the Pythagorean theorem which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): [tex]a^2 + b^2 = c^2[/tex].
Given that the distance from the pole to the point where the wire is attached to the ground (b) is 24 feet and the length of the wire (c) is 26 feet, we can set up the equation as follows:
[tex]24^2 + a^2 = 26^2[/tex]
576 + [tex]a^2[/tex] = 676
[tex]a^2[/tex] = 676 - 576
[tex]a^2[/tex] = 100
a = [tex]\sqrt{100}[/tex]
a = 10
Thus, the wire should be attached 10 feet up the pole.
Hiros family lives 448 kilometers from the beach.Each of the 5 adults drove the family van an equal distance to get to and from the beach.How far did each adult drive?
Answer:
179.2km
Step-by-step explanation:
The distance from their house to the beach is 448km. Now they have to drive to and from the beach. The total distance traveled by the family is 448km + 448km.
This is equal to 896km. Now we have 5 adults who took their turns to drive and they drove the same distance. The total distance traveled by each adult will be 896/5 = 179.2km
Hence, each adult in the family drove a distance of 179.2km
Marie used one bag of flour.She baked two loaves of bread.Each loaf required 2 1/4 cups of flour.Then she used the remaining 6 1/2 cups of flour to make muffins.How much flour was in the bag to begin with
Final answer:
Marie used 4 1/2 cups of flour for the bread and had 6 1/2 cups left for the muffins. By adding these amounts together, we find that the original bag of flour contained 11 cups of flour in total.
Explanation:
To determine how much flour was initially in the bag, we need to add together the amount of flour used for the bread and the muffins.
Marie baked two loaves of bread, with each loaf requiring 2 1/4 cups of flour. Therefore, the total flour used for bread is:
2 loaves × 2 1/4 cups/loaf = 4 1/2 cups
After baking the bread, she used the remaining 6 1/2 cups of flour to make muffins. To find the initial amount of flour in the bag, we add the flour used for the bread to the flour used for the muffins:
4 1/2 cups + 6 1/2 cups = 11 cups
Therefore, the bag originally had 11 cups of flour.
As the former chair of the planning board for 18 consecutive years and a board member for 28 years, Joan Philkill attended more than 400 meetings and reviewed more than 700 rezoning applications.
(A) As the former
(B) The former
(C) Former
(D) She was
(E) As the
Answer:
Option E is the correct answer (As the)
Step-by-step explanation:
Option A indicates that Joan, for 18 years, was the former chair; it is inappropriate to think that she would be attending meetings while she was the former chair. The sentence indicates that Joan served for 18 years as the chair lady, and during this time she attended meetings. Thus, option E is clearer and precise in its meaning than option A.
The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1515 and a standard deviation of 15. Approximately what percentage of buckets contain between 1470 and 1560 pieces of popcorn?
Approximately 68%
Approximately 75%
Approximately 95%
99.7%
Answer:
d: 99.7
Step-by-step explanation:
We know the mean is 1515. we know the standard devation is 15. both of 1560 and 1470 are both 3 standar devations away from the mean. on a table this would show almost all of the table. hence 99.7. Now im not 100% on this as i ahve the same question on a quiz but if i get it write i will add an answer or comment to this.
Percentage of buckets contain between 1470 and 1560 pieces of popcorn= 99.7%
How is percentage mean?percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
How do you calculate percentages?The following formula is a common strategy to calculate a percentage:
Determine the total amount of what you want to find a percentage. Divide the number to determine the percentage.Multiply the value by 100To learn more about percentage, refer
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What is the distance between (-3, 2) and (3, -8)?
The distance between (-3, 2) and (3, -8) is approximately 11.66.
Explanation:To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, (-3, 2) can be denoted as (x1, y1) and (3, -8) can be denoted as (x2, y2). Substituting these values in the formula:
d = sqrt((3 - (-3))^2 + (-8 - 2)^2)
d = sqrt(6^2 + (-10)^2)
d = sqrt(36 + 100) = sqrt(136)
The distance between (-3, 2) and (3, -8) is approximately 11.66.
Final answer:
To calculate the distance between (-3, 2) and (3, -8), one must find the differences in both the x and y coordinates, square these differences, sum them, and take the square root of this sum, which yields approximately 11.66.
Explanation:
To find the distance between the points (-3, 2) and (3, -8), we use the Pythagorean Theorem. The distance d is calculated as the square root of the sum of the squares of the difference in the x-coordinates and the y-coordinates.
First, find the differences:
Δx = [tex]x_2 - x_1[/tex] = 3 - (-3) = 6
Δy = [tex]y_2 - y_1[/tex] = -8 - 2 = -10
Then calculate the distance squared:
d² = (Δx)² + (Δy)²
d² = (6)² + (-10)²
d² = 36 + 100
d² = 136
Take the square root of the distance squared to find the distance:
d = [tex]\sqrt{136}[/tex]
d ≈ 11.66
On her plan, christina pays $5 just to place a call and $1 for each minute. When brenna makes an international call, she pays $1 to place the call and $5 for each minute. A call duration would cost exactly the same under both plans. What is the cost? What is the duration?
Answer:
$6 for a 1-minute call
Step-by-step explanation:
For duration "d" the costs of the plans are identical when ...
5 +1d = 1 +5d
4 = 4d . . . . . . . . add -1-1d to both sides
1 = d . . . . . . . . . divide by 4. Duration in minutes.
Then the cost for this 1-minute call is ...
5 + 1·1 = 6 . . . . dollars
Each plan will charge $6 for a 1-minute call.
Answer:
Step-by-step explanation:
Let x represent the call duration that would cost the same amount with either plans.
On her plan, christina pays $5 just to place a call and $1 for each minute. This means that the total cost of x minutes on this plan is
x + 5
When brenna makes an international call, she pays $1 to place the call and $5 for each minute. This means that the total cost of x minutes on this plan is
5x + 1
For both costs to be the same, the number of minutes would be
x + 5 = 5x + 1
5x - x = 5 - 1
4x = 4
x = 4/4 = 1
A call duration of 1 minute would cost exactly the same under both plans. The cost of the call would be
5 × 1 + 1 = $6
An airline, believing that 5% of passengers fail to show up for flights, overbooks (sells more tickets than there are seats). Suppose a plane will hold 265 passengers, and the airline sells 275 tickets. What’s the probability the airline will not have enough seats, so someone gets bumped?
Final answer:
To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight. The probability is 0.1525.
Explanation:
To find the probability that the airline will not have enough seats for passengers, we need to calculate the probability that more than 265 passengers show up for the flight.
First, we need to calculate the probability that a passenger shows up for the flight. Since the airline believes that 5% of passengers fail to show up, the probability that a passenger shows up is 1 - 0.05 = 0.95.
Next, we can use the binomial distribution to calculate the probability that more than 265 passengers show up. The formula for the binomial distribution is P(X > k) = 1 - P(X <= k), where X is the number of passengers who show up and k is the maximum number of passengers the plane can hold (265).
Using the binomial distribution, we can calculate the probability that more than 265 passengers show up as P(X > 265) = 1 - P(X <= 265) = 1 - binomcdf(275, 0.95, 265) = 0.1525.
If E(X)=100, E(Y)=120, E(Z) = 130, Var(X) = 9, Var(Y) = 16, Var(Z) = 25, Cov(X, Y)= - 10 Cov(X,Z) = 12, and Cov(Y,Z) = 14, then answer the followings: 1) Corr(X,Y) 2) Corr(X,Z) 3) Corr(Y,Z) 4) E(3X + 4Y – 3Z) 5) Var(3X – 3Z) 6) Var(3X + 4Y – 3Z) 7) Cov(3X, 2Y+3Z)
Answer:
(1) -0.833
(2) 0.80
(3) 0.70
(4) 390
(5) 90
(7) 48
Step-by-step explanation:
Given:
E (X) = 100, E (Y) = 120, E (Z) = 130
Var (X) = 9, Var (Y) = 16, Var (Z) = 25
Cov (X, Y) = -10, Cov (X, Z) = 12, Cov (Y, Z) = 14
The formulas used for correlation is:
[tex]Corr (A, B) = \frac{Cov (A, B)}{\sqrt{Var (A)\times Var(B)}} \\[/tex]
(1)
Compute the value of Corr (X, Y)-
[tex]Corr (X, Y) = \frac{Cov (X, Y)}{\sqrt{Var (X)\times Var(Y)}} \\=\frac{-10}{\sqrt{9\times16}} \\=-0.833[/tex]
(2)
Compute the value of Corr (X, Z)-
[tex]Corr (X, Z) = \frac{Cov (X, Z)}{\sqrt{Var (X)\times Var(Z)}} \\=\frac{12}{\sqrt{9\times25}} \\=0.80[/tex]
(3)
Compute the value of Corr (Y, Z)-
[tex]Corr (Y, Z) = \frac{Cov (Y, Z)}{\sqrt{Var (Y)\times Var(Z)}} \\=\frac{14}{\sqrt{16\times25}} \\=0.70[/tex]
(4)
Compute the value of E (3X+4Y-3Z)-
[tex]E(3X+4Y-3Z)=3E(X)+4E(Y)-3E(Z)\\=(3\times100)+(4\times120)-(3\times130)\\=390[/tex]
(5)
Compute the value of Var (3X-3Z)-
[tex]Var (3X-3Z)=[(3)^{2}\times Var(X)]+[(-3)^{2}\times Var (Z)]+(2\times3\times-3\times Cov(X, Z)]\\=(9\times9)+(9\times25)-(18\times12)\\=90[/tex]
(6)
Compute the value of Var (3X+4Y-3Z)-
[tex]Var (3X+4Y-3Z)=[(3)^{2}\times Var(X)]+[(4)^{2}\times Var(Y)]+[(-3)^{2}\times Var (Z)]+[(2\times3\times4\times Cov(X, Y)]+[(2\times3\times-3\times Cov(X, Z)]+[(2\times4\times-3\times Cov(Y, Z)]\\=(9\times9)+(16\times16)+(9\times25)+(24\times-10)-(18\times12)-(24\times14)\\=-230[/tex]
But this is not possible as variance is a square of terms.
(7)
Compute the value of Cov (3X, 2Y+3Z)-
[tex]Cov(3X, 2Y+3Z)=Cov(3X,2Y)+Cov(3X, 3Z)\\=6Cov(X, Y)+9Cov(X,Z)\\=(6\times-10)+(9\times12)\\=48[/tex]
The correct answers to the given set of data are:
(1) -0.8332) 0.80(3) 0.70(4) 390(5) 90(7) 48What is Variance?This refers to the measurement of spread between numbers which can be found in a set of data.
Hence, to compute the variance and covariance
E (X) = 100, E (Y) = 120, E (Z) = 130Var (X) = 9, Var (Y) = 16, Var (Z) = 25Cov (X, Y) = -10, Cov (X, Z) = 12, Cov (Y, Z) = 14Using the variance formula we can see that the given sets of data are:
-0.8330.800.703909048 respectivelyRead more about variance here:
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A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation 5. A e 95 percent confidence level? (A) with 100 confidence intervals, we can be95% co nfident that the sample proportion of citizens of the (B) We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the (C) We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of (D) Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from (E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sample United States who are optimistic about the economy
Answer:
Correct option (B).
Step-by-step explanation:
A 95% confidence interval for a population parameter implies that there is 0.95 probability that the population parameter is contained in that interval.
Or, if 100, 95% confidence intervals are created then 95 of those intervals would contain the population parameter with probability 0.95.
In this question the 95% confidence interval was created for population proportion of all United States citizens who were optimistic about the economy.
Then this 95% confidence interval implies that if 100 such confidence intervals were created then 95 of those would consist of the true proportion of US citizens who were optimistic about the economy..
Thus, the correct option is (B).
Answer:
We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.
Step-by-step explanation:
Kara is sorting buttons by lengths for a craft project.The line plot shows the length of each button.If Kara lines up all the 3/4-inche buttons,what would be the total length
Answer:
[tex]2\frac{1}{4} inches.[/tex]
Step-by-step explanation:
Hi,
We see the plot line below, which shows that three crosses above [tex]\frac{3}{4} - inch[/tex] buttons, that means we have three such buttons available with us.
To find their total lengths, we have two methods:
We can add the lengths of all buttons, that means add [tex]\frac{3}{4}[/tex] thriceOr simply multiply [tex]\frac{3}{4}[/tex] by three.[tex]\frac{3}{4} \times 3\\ = \frac{3 \times 3}{4}\\= \frac{9}{4}[/tex]
changing this improper fraction into a mixed fraction: [tex]2\frac{1}{4} inches.[/tex] will be the total length of three buttons lined up.
How many ounces of cinnamon is needed to bake cookies with 7 and 1/2 cups of flour if 1/3 ounce is cinnamon is needed for each 1 and 1/2 cups of flour?
Answer: 1 2/3 ounces of cinnamon is needed.
Step-by-step explanation:
1/3 ounce is cinnamon is needed for each 1 and 1/2 cups of flour. Converting 1 and 1/2 cups to improper fraction, it becomes 3/2 cups.
It means that the number of ounces of cinnamon need for 1 cup of flour would be
(1/3)/(3/2) = 1/3 × 2/3 = 2/9 ounces of cinnamon.
Converting 7 and 1/2 cups of flour to improper fraction, it becomes 15/2 cups of flour.
Therefore, the ounces of cinnamon needed to bake cookies with 15/2 cups of flour is
2/9 × 15/2 = 15/9 = 5/3
= 1 2/3 ounces of cinnamon
Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot. How much will it cost davis
Answer:
It will cost is $828.75.
Step-by-step explanation:
Given:
Davis is putting tile in his rectangular kitchen. His kitchen is 13 feet long, and 17 feet wide. The tile davis is installing is $3.75 per square foot.
Now, to find the total cost.
Davis is putting tile in his rectangular kitchen.
Length = 13 feet.
Width = 17 feet.
So, to get the area of kitchen:
Area = length × width
Area = 13 × 17
Area = 221 square foot.
As, the unit rate is given.
Cost per square foot = $3.75.
Now, to get the total cost by using unitary method:
If cost of 1 square foot = $3.75.
So, the cost of 221 square foot = $3.75 × 221
= $828.75.
Therefore, it will cost $828.75.
To find the total cost of tiling Davis' kitchen, we need to find the area of the kitchen in square feet by multiplying its length and width, then multiply the area by the cost per square foot. In this case, it will cost Davis $828.75 to tile his kitchen.
Explanation:The question is about Davis installing tiles in his rectangular kitchen and how much the cost will be at $3.75 per square foot. First, we need to determine the total area of the kitchen. In this case, the kitchen is rectangular in shape and the area of a rectangle is calculated by multiplying the length by the width. Here, length is 13 feet and the width is 17 feet, hence the area of the kitchen is 13 x 17 = 221 square feet.
Now, the cost per square foot of tile is given as $3.75. So, we multiply the total area by the cost per square foot to determine the overall cost of the tile. The calculation is as follows, 221 square feet x $3.75 = $828.75.
Therefore, it will cost Davis $828.75 to tile his kitchen.
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Jerry is buying a new large screen television for his game room.He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches.What is the area of the television (round to the nearest tenth)
Answer:
Step-by-step explanation:
The large screen television is rectangular in shape. The diagonal divides the rectangle into two equal right angle triangles. The diagonal represents the hypotenuse of the right angle triangle.
He knows that the diagonal of the television measures 42.1 inches and the base is 34.3 inches. To determine the height,h of the triangle which is also the width of the rectangle, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
42.1² = 34.3² + h²
h² = 1772.41 - 1176.49 = 595.92
h = √595.92 = 24.41 inches.
Area of rectangle = Length × width
Area of Television = 34.3 × 24.41 = 837.3 inches²
Ms Nelson will be teaching a group math lesson with counters frist she dumps out 4 bags that have 20 counters each then she divides the counter among 6 group of students
Answer:
13 r 3
Step-by-step explanation:
You can work a total of no more than 10 hours each week at your two jobs. Your house cleaning job pays $5. per hour and your sales job pays $8 per hours. You need to earn at least $56 each week to pay your bills.
Define your variables and write a system of inequalities that shows the number of hours you can work at each job.
System of inequalities are, [tex]x+y<10[/tex] and [tex]5x+8y\geq 56[/tex]
Let us consider, He does house cleaning job for x hours and sales job for y hours.
Since, he can work a total of not more than 10 hours each week at two jobs.
So, inequality are, [tex]x+y<10[/tex]
Since, house cleaning job pays $5. per hour and sales job pays $8 per hours.
Thus, Total earn = 5x + 8y
But he need to earn at least $56 each week
So, inequality are , [tex]5x+8y\geq 56[/tex]
Learn more:
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Final answer:
The variables x and y represent the hours worked at the house cleaning and sales jobs, respectively. The system of inequalities x + y ≤ 10, 5x + 8y ≥ 56, and x ≥ 0, y ≥ 0 reflects the constraints on work hours and minimum earnings.
Explanation:
To solve the problem, we need to define two variables representing the hours worked at each job:
Let x be the number of hours worked at the house cleaning job.
Let y be the number of hours worked at the sales job.
Given the conditions of the problem, we can formulate the following system of inequalities:
The total working hours from both jobs cannot exceed 10 hours per week: x + y ≤ 10.
The total earnings must be at least $56 to pay bills: 5x + 8y ≥ 56.
The number of working hours cannot be negative: x ≥ 0 and y ≥ 0.
This system of inequalities represents the constraints on the number of hours you can work at each job and the minimum earnings required to pay your bills.
The legs of a right triangle are x and 15 while the hypotenuse is 17.
Which equation can be used to determine the value of x using the Pythagorean Theorem?
Answer:
Since the Option of equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Step-by-step explanation:
Given:
Length of One leg = x
Length of other Leg= 15
Hypotenuse = 17
We need to find the equation used to determine the value of x.
Solution:
Assuming Triangle to right angled triangle.
So we will apply Pythagoras theorem which sates that;
"The square of sum of two legs of right angle triangle is equal to square of the length of hypotenuse."
so we can say that;
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Since the equation are not given. Kindly chose any of the below equation from the answer to find the value of 'x'.
[tex]x^2+15^2=17^2[/tex]
[tex]x^2=17^2-15^2[/tex]
OR
[tex]x^2+225=289[/tex]
[tex]x^2=289-225[/tex]
Answer:
b
Step-by-step explanation:
The bill for five glasses of apple juice and four salads is $9.50, but the bill for four glasses of apple juice and five salads is $10.30. What would be the bill for a glass of juice and a salad?
Answer: the bill for a glass of apple juice is $0.7 and the bill for a salad is $1.5
Step-by-step explanation:
Let x represent the bill for a glass of apple juice.
Let y represent the bill for a salad.
The bill for five glasses of apple juice and four salads is $9.50. It means that
5x + 4y = 9.5 - - - - - - - - - - - 1
The bill for four glasses of apple juice and five salads is $10.30. This means that
4x + 5y = 10.30- - - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 5, it becomes
20x + 16y = 38
20x + 25y = 51.5
Subtracting, it becomes
- 9y = - 13.5
y = - 13.5/-9
y = 1.5
Substituting y = 1.5 into equation 1, it becomes
5x + 4 × 1.5 = 9.5
5x + 6 = 9.5
5x = 9.5 - 6 = 3.5
x = 3.5/5 = 0.7
The bill for a glass of juice and a salad would be $2.20.
Explanation:To find the cost of a glass of apple juice and a salad, we need to set up a system of equations using the given information. Let's assign variables to the cost of a glass of apple juice and a salad. Let x be the cost of a glass of apple juice and y be the cost of a salad.
From the first sentence, we can write the equation 5x + 4y = 9.50. From the second sentence, we can write the equation 4x + 5y = 10.30.
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. Multiply the first equation by 4 and the second equation by 5 to eliminate x:
20x + 16y = 38.00
20x + 25y = 51.50
Subtract the first equation from the second:
9y = 13.50
Divide both sides by 9:
y = 1.50
Substitute this value of y into one of the original equations (let's use the first equation):
5x + 4(1.5) = 9.50
5x + 6 = 9.50
Subtract 6 from both sides:
5x = 3.50
Divide both sides by 5:
x = 0.70
Therefore, the bill for a glass of juice and a salad would be $0.70 + $1.50 = $2.20.
Which choice is equivalent to the quotient shown here when x>0?
Answer:
The answer to your question is letter C.
Step-by-step explanation:
[tex]\sqrt{50x^{3}}[/tex] Find the prime factors of 50
50 2
25 5
5 5
1
50 = 2 5²
[tex]\sqrt{5^{2} 2 x^{2} x} = 5 x\sqrt{2x}[/tex]
[tex]\sqrt{32x^{2}}[/tex] Find the prime factors of 32
32 2
16 2
8 2
4 2
2 2
1
32 = 2⁴2[tex]\sqrt{32x^{2}} = 2^{2} x\sqrt{2} = 4x\sqrt{2}[/tex]
Division [tex]5x\sqrt{2}\sqrt{x} / 4x\sqrt{2}[/tex]
Simplification [tex]\frac{5\sqrt{x}}{4}[/tex]
Answer:
C
Step-by-step explanation:
A P E x
which of the following is the product of the rational expressions shown below? 7x/x-4•x/x+7
Step-by-step explanation:
We have,
[tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
To find, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex] = ?
∴ [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7}[/tex]
= [tex]\dfrac{7x.x}{(x-4)(x+7)}[/tex]
= [tex]\dfrac{7x^2}{(x(x+7)-4(x+7)}[/tex]
= [tex]\dfrac{7x^2}{x^2+7x-4x-28}[/tex]
= [tex]\dfrac{7x^2}{x^2+3x-28}[/tex]
Thus, the product of the rational expressions [tex]\dfrac{7x}{x-4}.\dfrac{x}{x+7} = \dfrac{7x^2}{x^2+3x-28}[/tex].
Let w represent Henry's weight in pounds. Eric weighs 12 pounds less then Henry. Write an algebraic expression that represents Eric's weight in pounds.
Answer:
Step-by-step explanation:
w = Henry's weight
e = Eric's weight
e = w - 12
The algebraic expression that represents Eric's weight in pounds is [tex]\( w - 12 \)[/tex].
1. We're given that [tex]\( w \)[/tex] represents Henry's weight in pounds. This means we're using the variable [tex]\( w \)[/tex] to stand for whatever Henry's weight is.
2. The problem states that Eric weighs 12 pounds less than Henry. So, if Henry weighs [tex]\( w \)[/tex] pounds, then Eric's weight would be [tex]\( w - 12 \)[/tex] pounds because he's 12 pounds lighter than Henry.
3. Therefore, the expression [tex]\( w - 12 \)[/tex] represents Eric's weight in pounds. We subtract 12 from Henry's weight [tex]\( w \)[/tex] to get Eric's weight. This expression tells us Eric's weight in terms of Henry's weight.
Final total cost of making a triangular sale that has a base dimension of 12 feet and the height of 25 feet if the price for making the sale is $19.50 per square foot
Answer:
$2925
Step-by-step explanation:
To find the cost, we need to get the area of the triangular sale. This can be obtained by using the area of a triangle.
This is A = 1/2 * b * h
Where in this case, b = 12ft and h = 25ft
The area is thus 1/2 * 12 * 25 = 150sq.ft
Now we know that 1sq.ft is $19.50, 150 will be 150 * 19.5 = $2925
Help please
Find the area of the following figure: (Do NOT include the units in your answer...only type the numerical portion of your answer!)
Answer:
84
Step-by-step explanation:
Area of a rectangle : A = bh
5 x 6 = 30
Area of a trapezoid : A = 1/2 (b1 + b2) h
b1: 7 + 5 = 12
b2: 15
h: 10 - 6 = 4
12 + 15 = 27
27 x 4 x .5 = 54
Add the areas up:
30 + 54 = 84
A police report shows that 82% of drivers stopped for suspected drunk driving receive a breath test, 34% receive a blood test, and 24% receive both tests. What's the probability that a randomly selected DWI suspect receives neither test
Answer:
0.08
Step-by-step explanation:
If 8% of drivers receive neither test, then the probability = 8/100 = 0.08
Final answer:
The probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%, determined by subtracting the combined probability of receiving at least one test (92%) from 1.
Explanation:
Calculating the Probability of Receiving Neither Test
To determine the probability that a DWI (driving while intoxicated) suspect receives neither a breath test nor a blood test, we can use the principle of inclusion-exclusion from probability theory. According to the police report, 82% receive a breath test, 34% receive a blood test, and 24% receive both tests.
Firstly, we need to find the probability of a suspect receiving at least one test. We add the probabilities of receiving each test and subtract the probability of receiving both tests to avoid double-counting:
P(Breath or Blood Test) = P(Breath) + P(Blood) - P(Both)
= 0.82 + 0.34 - 0.24
= 0.92
This means that 92% of DWI suspects receive at least one test. To find the probability that a suspect receives neither test, we subtract this value from 1 since the sum of the probabilities of all possible outcomes must equal 1:
P(Neither) = 1 - P(Breath or Blood Test)
= 1 - 0.92
= 0.08 or 8%
Hence, the probability that a randomly selected DWI suspect receives neither a breath test nor a blood test is 8%.
Suppose that the height(In centimeters) Of a candle is a linear function of time (in hours) it has been burning. After seven hours of burning, a candle has high of 22.5 Centimeters. After 26 hours of burning, it's high is 13 cm. What is the height of the candle after 10 hours
Answer: the height after 10 hours is 21 cm
Step-by-step explanation:
Assuming the rate at which the height of the candle is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
If after seven hours of burning, a candle has high of 22.5 Centimeters, the expression is
22.5 = a + (7 - 1)d
22.5 = a + 6d - - - - - - - - - -1
If after 26 hours of burning, it's height is 13 cm. The expression is
13 = a + (26 - 1)d
13 = a + 25d - - - - - - - - - - - 2
9.5 = - 19d
d = 9.5/ - 19
d = - 0.5
Substituting d = - 0.5 into equation 1, it becomes
22.5 = a + 6 × - 0.5
22.5 = a - 3
a = 22.5 + 3
a = 25.5
The linear expression becomes
Tn = 25.5 - 0.5(n - 1)
The height of the candle after 10 hours would be
25.5 - 0.5(10 - 1)
= 25.5 - 4.5
= 21 centimeters
sinusoidal wave in a string is described by the wave function y 5 0.150 sin (0.800x 2 50.0t) where x and y are in meters and t is in seconds. The mass per length of the string is 12.0 g/m. (a) Find the maximum transverse acceleration of an element of this string. (b) Determine the maximum transverse force on a 1.00-cm segment of the string . (c) State how the force found in part (b) compares with the tension in the string
Answer:
a) 375m/s2
b) F = 0.045N
c) F/T = 0.00096
d) Tension = 46.9N
Step-by-step explanation:
The step by step calculation is as shown in the attached file.