The area of the rectangle is 18 square units if the vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1).
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
It is defined as the two-dimensional geometry in which the angle between the adjacent sides is 90 degrees. It is a type of quadrilateral.
It is given that:
A rectangle with vertices at a (−6, 3) , b (−3, 6) , c(1, 2) , and d(−2, −1)"
As we know,
The distance formula can be given as:
[tex]\rm d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
ab = √(x₁-x₂)²+(y₁-y₂)²
=√(-6+3)²+(3-6)²
= √18
cd =√(1+2)²+(2+1)²
= √18
Area= lxw
A=√18x√18
a=18
Thus, the area of the rectangle is 18 square units if the vertices at (−6, 3) , (−3, 6) , (1, 2) , and (−2, −1).
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PLEASE HELP ME ASAP!!!
1. The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score of glass cleaner with a cost of 10.1 cents per ounce?
A. 0.96
B. 1.31
C. 1.94
D. 4.04
E. none of the above
2. A candy bar takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hours, what is the probability that the candy bar will take between 3 and 4 hours to move through the line?
A. .2119
B. .2295
C. .6731
D. .3270
E. .8849
3. The average noise level in a diner is 30 decibels with a standard deviation of decibels. 99% of the time, the noise level is below what value?
A. 16.04
B. 30.00
C. 36.00
D. 43.96
E. 48.00
4. The mean income per household in a certain state is $29,500 with a standard deviation of $5,750. The middle 95% of incomes is between what two values? The incomes are normally distributed.
A. $23, 750 and $35,250
B. $18,000 and $41,000
C. $29,500 and $41,000
D. $12,250 and $46,750
E. $12,325 and $81,550
Final answer:
The student's questions involve calculating z-scores and applying knowledge of normal distributions to determine probabilities and percentile ranges within a set of data. Correct answers include finding the z-score for glass cleaner costs, determining the probability of assembly line time for a candy bar, identifying the noise level not exceeded 99% of the time in a diner, and calculating the income range for the middle 95% in a state.
Explanation:
To solve these problems related to standard normal distribution and probabilities, we'll follow a step-by-step process. For each question, you'll either need to calculate a z-score or apply knowledge of normal distributions.
The z-score for a glass cleaner costing 10.1 cents per ounce when the mean cost is 7.7 cents and the standard deviation is 2.5 cents is calculated as: z = (10.1 - 7.7) / 2.5 = 0.96. The correct answer is A.The probability of a candy bar taking between 3 and 4 hours through the assembly line involves finding the area under the normal curve between these two z-scores: z for 3 hours and z for 4 hours. Use z-tables or calculators to find P(3 < X < 4) = P(Z < (4 - 3.4) / 0.5) - P(Z < (3 - 3.4) / 0.5) which gives us C. 0.6731.To find the noise level that is not exceeded 99% of the time, use the z-score that corresponds to 99% in the standard normal distribution and multiply by the standard deviation and add to the mean. This gives us 43.96 decibels, with D being the correct answer.The middle 95% of normally distributed incomes is found using z-scores that correspond to the 2.5th percentile and 97.5th percentile because 95% is in between. The correct answer is A. $18,000 and $41,000.Boats can travel anywhere between 50 and 150 kilometers per hour. Choose a speed between 50 and 150. Convert the speed you chose into meters per second and explain how you set up the conversion factor.
Gail owns a small business. There was a profit of $43 on Saturday and a loss of $48 on Sunday. Find the total profit or loss for the weekend.
A) $5 profit
B) $5 loss
C) $91 loss
D) $91 profit
find the product of (a²+b)(2a²-5b)
Three interior angles of a quadrilateral measure 55, 117 and 120 degrees. What is the measure of the fourth interior angle?
4 angles = 360
120 + 117 +55 = 292
360-292 = 68
4th angle = 68 degrees
What is 12.1167 rounded to the nearest hundredth?
I really need help doing this spelling plz answer really Quick
A. Matching Definitions:
1 small whirls - eddies
2. snake teeth - fangs
3. rattlesnakes - rattles
4. defeats; failures - losses
5. freedoms - liberties
6. skills; talents - abilities
7. bunches or groups - batches
8. eyelid hairs - lashes
9. nations - countries
10. accepted truths - beliefs
How to perform the completing sentences11. The cook put potatoes and carrots in the stew.
12. Are crocodiles and alligators reptiles?
13. Many rodeos have riding and roping events.
14. The travelers were happy in their new surroundings.
15. Our taxes will be used to build new schools.
16. The numeral 100 has two zeroes.
17. He searched the paper for job opportunities.
18. You can use an ax to put notches in a log.
19. The clever criminal had many different identities.
20. Pioneers faced many difficulties in the wilderness.
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-7+n/5= -11 can someone help me I'm bad a math
PLEASE HELP ME!!! WORTH 10 POINTS!!!
Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (1, 2). Use the box provided or the upload option to submit all of your calculations and final answer.
How to know if a line is parallel perpendicular or neither?
How many diagonals can be drawn from one vertex of a hexagon
Nine diagonals can be drawn from the vertex of a hexagon.
What is diagonal?A diagonal of a polygon is a line segment joining two vertex points, excluding the sides of the polygon.
The formula used to find the number of diagonals of a polygon is
(n(n-3))/2
where n is the number of sides of the polygon.
A hexagon has six sides. So, n=6.
The number of diagonals in a hexagon is given by
(6(6-3))/2=9
Hence, a hexagon has nine diagonals.
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Find the volume of a cube that will hold sixty-four 4.19 in3 toy bouncy balls. (round to nearest whole number)
we know that
The volume of the ball (sphere) is equal to
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
In this problem we have
[tex]V=4.19\ in^{3}[/tex]
Find the radius of the sphere
[tex]r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Substitute the value of V
[tex]r=\sqrt[3]{\frac{3*4.19}{4\pi}}=1\ in[/tex]
for the calculation of the total volume I will assume that each ball is a cube
The volume of each ball is
[tex]V=b^{3}[/tex]
where
b is the diameter of the ball
[tex]b=1*2=2\ in[/tex]
Substitute
[tex]V=2^{3}=8\ in^{3}[/tex] ------> volume of each ball in the shape of cube
so
Multiply by [tex]64[/tex]
[tex]64*8=512\ in^{3}[/tex]
therefore
the answer is
[tex]512\ in^{3}[/tex]
the recommended dosage of a drug for pediatric patients is 200 mg per kilogram of a patients weight if janine weights 76lb how much of the drug should she get
To determine the dosage of a drug for Janine, who weighs 76 pounds, convert her weight to kilograms and then multiply by the recommended dose per kilogram. The conversion and the dose calculation led to approximately 6894.6 mg of the drug.
The recommended dosage of a drug for pediatric patients is 200 mg per kilogram of the patient's weight. To calculate the dosage for Janine, who weighs 76 pounds, we first need to convert her weight from pounds to kilograms, as dosages are usually measured in metric units. To do so, we use the conversion factor where 1 kilogram equals 2.20462 pounds.
First, we convert Janine's weight to kilograms:
[tex]\frac{76}{2.20462}[/tex] lb/kg = 34.473 kg roughly.
Next, we calculate the total dosage needed in milligrams by multiplying her weight in kilograms by the dosage per kilogram:
34.473 kg * 200 mg/kg = 6894.6 mg.
Therefore, Janine should receive a dose of approximately 6894.6 mg of the drug.
for lunch , you must choose a sandwich, a piece of fruit, and a drink. your choices include a ham sandwich, tuna sandwich, or cheese sandwich; an apple or an orange; and skim milk, whole milk, fruit juice, or bottle water. how many combinations of choices are possible
What is 4.14 trillion in scientific notation?
The given data can be written in scientific notation as 4.14 × 10¹².
How to write a number in scientific notation?In order to write a number in scientific notation, express the number in terms of the product of a number between 0 to 10 and the power of 10.
For example, 32 can be written as 3.2 × 10¹.
Here, 3.2 is between 0 and 10 and the power of 10 is 1
The given data is 4.14 trillion.
Since, one trillion can be written as,
1 trillion = 1,000,000,000,000
The number of zeros is 12.
In the scientific notation 4.14 trillion can be written as below,
4.14 × 10¹²
Hence, the scientific notation of the given data is 4.14 × 10¹².
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if f(x)= 5x +40 what is f(x) when x= -5
Which of the following is the quadratic parent function
Answer:
A. F(x)=x^2
Step-by-step explanation:
Answer: Option A F(x)=[tex]x^{2}[/tex]
Explanation:
Quadratic function is the function which has degree two
Degree is the highest power of a polynomial
In option B we have |x| in which degree is one hence, discarded
In option C we have [tex]x^{3}[/tex] in which degree is three hence, discarded
In option D we have x which is a linear function being of degree one. Hence, discarded.
HELPS ASAP PLEASE!!!!
Find the product of -9 and -3.
A. 27
B. -27
C. 3
D. -3
5c+2(10−c) ????????
(x+8) - (X-8) ?????
Find the real roots of the equation x^4-5x^2-36=0
Use implicit differentiation to find the slope of the tangent line to the curve 4 x^2 - 3 xy + 4 y^3 = -113 at the point ( -1,-3 ).
If the width of the rectangle is three times the length and the perimeter of the rectangle is 72 ft, what are the length and width of the rectangle?
You are dealt one card from a 52-card deck. find the probability that you are not dealt: a heart.
What is the value of x in the equation below?
–3 – (–8) – (–2) = x
If I'm not mistaken (it's been a while since I was in school) I believe the answer is x=11.
Samantha is planting a garden in her backyard that is going to be 600 square inches. She loves tomatoes and wants them to cover 60% of the garden. She then put lettuce in 1/3 of what was left. The remaining part of her garden was used for fresh herbs. What is the area of the garden that is fresh herbs?
What is 2 1/5, 2.25, 8/20, 2.8 all
from least to greatest
Quadratic inequalities
How many people lost their jobs when minimum wage increased from $12 to $18?
Answer:
15 people lost their jobs when minimum wage increased from $12 to $18
Step-by-step explanation:
When the minimum wage is $12
Then by looking at the given graph :
Number of labors supplied = 33
Number of labors in demand = 33
So, it is an equilibrium wage for the system.
Now, when the minimum wage increased from $12 to $18
From the given graph :
Number of labors supplied = 45
Number of labors in demand = 18
⇒ Number of labors working when wage is $12 = 33
And when the wage is $18, no. of labors working or are in demand = 18
⇒ Number of workers who lost their job = 33 - 18 = 15
Hence, 15 people lost their jobs when minimum wage increased from $12 to $18
Write an algebraic expression for the phrase. 8 times the quantity d minus 3 8d – 3 8(d – 3) d(8 – 3)
what are the zeros of f(x)=x^2+7x+5